Alternating Current | Visual Physics for IIT JEE / NEET
Alternating Current

What is Alternating Current ? How is Alternating current different from Direct Current ? Is it just a theoretical concept or does it have any practical application ? How do we create Alternating Current ?

Phasor

Are Alternating Voltages and Currents always in Phase ? i.e do they reach their maximum and minimum values at the same time ? If they are not in phase, how do we deal with such a complex situation ?

Q1

The figure shows 4 sine curves and 4 phasors. Phase difference between two corresponding waves is f. Which curve corresponds to which phasor ? If we take the curve C as reference, then a) then which curves lead, which curves lag ? b) which curves has positive / negative phase difference ? c) write the equation of other curves.

Average and RMS

What is a more important value for alternating voltage and current, their average or RMS value ?

Q2

Two sinusoidal voltages of same frequency are shown in figure What is the phase lead of B over A ? What will be the minimum time required for the voltage of A to change from its RMS value to its maximum value ?

Q3

A dc ammeter and a hot wire ammeter are connected to a circuit in series. When a direct current is passed through circuit, the dc ammeter shows 6A. When ac current flows through circuit, the ac ammeter shows 8A. What will be reading of each ammeter if dc and ac currents flow simultaneously through the circuit ?

Q4

Voltage supplied by a source switches rapidly between + a and - a, as shown in figure. What will be the reading of a DC Voltmeter and AC Voltmeter ? The current - time graph for triangular wave having peak value a is as shown in figure. What will be the reading of a DC Ammeter and AC Ammeter ?

Resistive Load

How is Alternating Current related to an Alternating Voltage when it is applied across a Resistor ? Will their Phase be the same ? Will their Amplitude be the same ? Can the Amplitude of Alternating current be more than the Amplitude of Alternating Voltage ?

Capacitive Load

How is Alternating Current related to an Alternating Voltage when it is applied across a Capacitor ? Will their Phase be the same ? Will their Amplitude be the same ? Can the Amplitude of Alternating current be more than the Amplitude of Alternating Voltage ?

Inductive Load

How is Alternating Current related to an Alternating Voltage when it is applied across an Inductor ? Will their Phase be the same ? Will their Amplitude be the same ? Can the Amplitude of Alternating current be more than the Amplitude of Alternating Voltage ?

Q5

An AC source is connected to either a Resistor, Inductor or Capacitor, at t = 0. At t = 2 sec, voltage and current in the circuit are measured to be 10 V and 2 A respectively. If the source is connected to a resistor, can we find the resistance from the given information ? If the source is connected to inductor or capacitor, can we find the reactance from the given information ?

Q6

In the circuit shown in figure , resistance R, inductor L, and capacitor C is connected to a 100 V, 50 Hz ac source of negligible resistance. With either key k1 alone, k2 alone or k3 alone closed, the current is Io. If the frequency of source is changed to 100 Hz, then what will be the current with key k1 alone, k2 alone or k3 alone closed, respectively ?

Series RL Circuit - 1

How is Alternating Current related to an Alternating Voltage when it is applied across a series combination of a Resistor and an Inductor (Series RL Circuit) ? Will the current Lead or Lag voltage ? Will the variation of Voltage across Resistor and Inductor be in Phase ? Discover the easier and more intuitive methods of Voltage and Impedance Triangles discussed in this video.

Series RL Circuit - 2

Mathematical Derivation of the equations of Series RL Circuit.

Q7

a) A 220 V, 50 Hz ac generator is connected to an inductor and a 50 W resistance in series. The current in the circuit is 1 A. What is the potential difference across inductor ? What is the phase difference between current and voltage of source ? b) A 220 V, 50 Hz ac generator is connected to an inductor and a resistance in series. Phase difference between current and voltage of source is given to be 60o. What is the potential difference across Inductor and Resistor ? What is the amplitude of current in circuit ? If it is given that resistance is 100 W , can we find the amplitude of current ?

Q8

A long wire of finite resistance is connected to an ac generator. This wire is then wound into a coil of many loops and reconnected to the generator. Is the current in the circuit with the coil, greater than, less than, or the same as the current in the circuit with the uncoiled wire ? Now when the above coil is connected to an ideal battery of emf 10 V, a constant current 2.5 A flows. When the same coil is connected to an ac source with voltage amplitude of 10 V and 50 Hz then the current is 2 A. Find the inductance of coil.

Q9

In an L - R series circuit, a sinusodial voltage v = Vo sin wt is applied. It is given that L = 35 mH, R = 11 W, Vrms = 220 V, w/2p = 50 Hz and p = 22 / 7. Find the amplitude of current in the steady state and the phase difference between the current and the voltage. Write the equation of current through the circuit.

Series RC Circuit

How is Alternating Current related to an Alternating Voltage when it is applied across a series combination of a Resistor and a Capacitor (Series RC Circuit) ? Will the current Lead or Lag voltage ? Will the variation of Voltage across Resistor and Capacitor be in Phase ? Discover the easier and more intuitive methods of Voltage and Impedance Triangles discussed in this video.

Q10

A series R-C combination is connected to an AC voltage of angular frequency w rad/s. If the impedance of the R-C circuit is ?1.25 R , then time constant of the circuit is ?

Q11

In an RC series circuit, the rms voltage of source is 200 V and its frequency is 50 Hz. If R = 100 W and C = 100/ p mF, find

Series LC Circuit

How is Alternating Current related to an Alternating Voltage when it is applied across a series combination of an Inductor and a Capacitor (Series LC Circuit) ? Will the current Lead or Lag voltage ? Will the variation of Voltage across Capacitor and Inductor be in Phase ? Discover the easier and more intuitive methods of Voltage and Impedance Triangles discussed in this video.

Q12

A radio can be tuned over a frequency range from 500 kHz to 1.5 MHz. If its L-C circuit has an inductance of 400 mH, what is the range of its variable capacitance ?

Q13

When an AC source with voltage v (t) = Vo sin ( 100 t ) is connected across a circuit. Voltage in circuit is observed to be ahead of current i by a phase of p/4 , as shown in the diagram. If the circuit consists possibly only of R - C or R - L or L - C in series, find the relationship between the two elements

Q14

You are given many resistances, capacitors and inductors. These are connected to a variable DC voltage source ( the first two circuits) or an AC voltage source of frequency 50 Hz ( the next three circuits) in different ways as shown in column II. When a current I (steady state for DC or rms for AC) flows through the circuit, the corresponding voltage V1 and V2 (indicated in circuits) are related as shown in Column I. Match the conditions in column I with the circuits in column II

Q15

For the circuit shown in figure, find the amplitude of current through source, phase between the voltage and current through source, and the equation of current through source.

Q16

In the circuit shown below, a resistor and an inductor are connected in parallel to an alternating voltage source. Will the amplitude of current supplied by source ( Io ) and phase between current and voltage (?? ) increase / decrease by increasing / decreasing the angular frequency w, inductance L, resistance R ? What will the value of Io and f approach for very low and very high values of angular frequency ? Repeat the above question for a parallel R - C circuit.

Q17

An inductor and a capacitor are connected in parallel to an AC source. Find the expression of amplitude of current through source. What happens when XL = XC ?

Q18

For the circuit shown in figure, the ammeter A2 reads 1.6 A and ammeter A3 reads 0.4 A . What is the frequency of source ? If frequency of the oscillator is varied while voltage amplitude of source is fixed, then which curve in figure corresponds to the variation of amplitude of current in A1, A2 and A3 ? If L or C is increased / decreased, does the point P shift towards left / right ?

Series RLC Circuit

How is Alternating Current related to an Alternating Voltage when it is applied across a series combination of a Resistor, a Capacitor and an Inductor (Series RLC Circuit) ? Will the current Lead or Lag voltage ? Will the variation of Voltage across Resistor and Inductor be in Phase ? Discover the easier and more intuitive methods of Voltage and Impedance Triangles discussed in this video.

Q19

For a series RLC circuit connected to an AC source, following information is available to us. What will be the amplitude of current in circuit ?

Q20

The generator delivers ? times more current at very low frequencies than it does at very high frequencies as shown in figure. Find the ratio of R2/R1 of the resistance.

Q21

A 20 mF capacitor, a 1 H inductor and a 300 W resistor are connected in series with an ac source of emf vo (t) = 300 sin(100 t). Find a) the frequency of source b) the reactance of the circuit c) the impedance of the circuit d) the current in the circuit e) the phase angle f) the effective voltages across the capacitor, inductor, and resistor

Q22

In a series LRC circuit connected to an AC source, can the amplitude of voltage across inductor be more than the amplitude of voltage of source ? can the amplitude of voltage across capacitor be more than the amplitude of voltage of source ? can the amplitude of voltage across both the inductor as well as capacitor be more than the amplitude of voltage of source ? If yes, then find the conditions for each case.

Q23

In series LCR circuit, voltage drop across resistor, capacitor and inductor, respectively, is as below i) 8 V, 12 V, 6 V ii) 8 V, 18 V, 12 V iii) 8 V, 10 V, 4 V If capacitor is removed, then a) will the phase angle increase / decrease / remain the same b) will the current in circuit increase / decrease / remain the same

Q24

A series RLC circuit is driven by a generator at frequency Hz. The inductance is 100 mH; the capacitance is 2 mF; and the phase constant is given by ( you should supply the appropriate sign for the angle ). a) what is the resistance? To increase the amplitude of current in the circuit, should we increase or decrease b) the driving frequency c) the inductance d) the capacitance

Q25

Current in two series LCR circuits at resonance is same. Then a) both circuits must be having same value of capacitance and inductance b) in both circuits ratio of L and C will be same c) for both the circuits XL / XC must be same at that frequency d) both circuits must have same impedance at all frequencies e) ratio of resistances in the circuits will be = the ratio of the voltage amplitude of sources

Q26

A series RLC circuit is connected to an AC source of variable frequency. Current amplitude in the circuit has the same value at frequencies w1 and w2 . Find the resonance frequency.

Q27

For the circuit shown in figure, find the instantaneous current through each element. Also find (a) the total instantaneous current through the source and (b) the expression for the phase angle of this current and the impedance of the circuit.

Power - 1

How does Power vary in a circuit with Alternating Voltage and Alternating Current ? Can energy be absorbed back by the power source ? Is power dissipated in AC circuit the same that in DC circuit ?

Power - 2

Power variations when an AC source is applied across Resistor, Capacitor and Inductor ? Can power be virtual ? Can energy be absorbed back by the power source ?

Q28

The element of an electric heater is in the form of a coil. Once it is heated by DC source and then by AC source of equal effective voltage. Will the production of heat in both cases be same or different ? If the voltage of DC source is = V , what should be effective voltage of AC source if the rate of heat dissipation in coil is to be equal to that in case of DC source ? For the initial case, where effective voltage of AC source is = the voltage of DC source, at what frequency of AC source will the power consumed by the coil be h times less than in case of DC source ?

Q29

An AC source has angular frequency w. What will be angular frequency of oscillation of output power ?

Q30

At Resonance in a series LRC circuit, which of the following is true ? a) angular frequency of the source is equal to 1/ LC b) capacitive and inductive reactances of the circuit are equal c) current in the circuit is maximum d) power transferred to the resistor is maximum e) power factor is = 1

Q31

The power factor of the given circuit is 1/ 2 What will be the capacitance of the circuit ?

Q32

An AC voltage source of variable angular frequency w and fixed amplitude Vo is connected in series with a capacitance C and an electric bulb of resistance R (zero inductance). Will the bulb become brighter / dimmer a) when w is increased / decreased b) when a dielectric is placed inside the capacitor c) when R is increased / decreased An AC voltage source of variable angular frequency w and fixed amplitude Vo is connected in series with an inductance L and an electric bulb of resistance R. Will the bulb become brighter / dimmer a) when w is increased / decreased b) when a soft iron core is placed inside the inductor<>br c) when R is increased / decreased

Q33

In a sinusoidally driven series RLC circuit the current lags the applied emf. The rate at which energy is dissipated in the resistor can be increased by a) decreasing the capacitance b) increasing the capacitance c) decreasing the inductance d) increasing the inductance e) decreasing the driving frequency f) increasing the driving frequency g) decreasing the amplitude of driving emf h) increasing the amplitude of driving emf If the ac frequency is i) increased to a very large value j) decreased to a very small value what value does the phase angle between the current and voltage approach?

Q - Factor

How does a Radio Tuner work ? What is Resonance in Electrical Circuits ? And what is Qfactor ? And is it related to Resonance ?

Q34

What is the resonant frequency and Q-factor of a series LCR circuit with L = 1 H, C = 1 mF, and R = 10 W. How can you improve the sharpness of resonance curve of the circuit by a factor of 2 without changing the resonance frequency ?

Q35

a) In LCR circuit, half power frequencies are at 620 and 580 Hz. What is the quality factor ? b) In LCR circuit, quality factor Q = 100. At a certain frequency, power generated in the circuit reaches maximum value. How much (in percent) should this frequency be shifted to reduce the power generated to half of its maximum value ?

Transformer

Is electricity generated at 240 Volts and transmitted to our homes ? Why do we require transformers ? And how do Transformers work ?

Q36

The primary coil of an ideal transformer has 100 turns and the secondary coil has 500 turns. Then (a) the power in the primary circuit is less than that in the secondary circuit (b) the currents in the two circuit are the same (c) the voltage in the two circuit are the same (d) the primary current is 5 times the secondary current (e) the frequency in the secondary circuit is 5 times that in the primary circuit

1

In a series R-L circuit connected to an AC source, if resistance increases by a factor of h , then by what factor should inductance change so that the phase angle f between the voltage and current of source remains the same ?By what factor does the current change in the above process?

2

In the circuit given in figure, VC = 50 V and R = 120 W . Find the values of C and VR

3

An AC source of angular frequency w is fed across a resistor R and a capacitor C in series. Peak current in circuit is I. If now the frequency of source is changed to w/3 (but maintaining the same voltage), the current in the circuit is found to be halved. Calculate the ratio of the reactance to resistance at the original frequency w.

4

Two resistors are connected in series across an AC source with peak voltage = 5 V. The potential difference across 6 W resistor is 3 V. If R is replaced by a pure inductor L of such magnitude that current remains same, then find the potential difference across L.

5

An ideal choke takes a current of 10 A when connected to an ac supply of 125 V and 50 Hz. A pure resistor connected to the same source takes a current of 12.5 A. If the choke and resistor are connected in series to an ac supply of 100 V and 40 Hz, find the current in circuit.

6

In an ideal transformer (assumed to be 100% efficient), ratio of the secondary turns to the primary turns 1 : 10 . A 300 V ac supply is connected to the primary coil and a 60 W resistor is connected to the secondary coil . What is the current in the primary coil?

7

A typical light dimmer consists of a variable inductor L (whose inductance is adjustable between zero and Lmax ) connected in series with a light bulb. The mains electrical supply is 220 V at 50 Hz, the light bulb is rated at 220 V, 1100 W. What Lmax is required if the rate of energy dissipated in the light bulb is to be varied by a factor of 5 from its upper limit of 1100 W ?

8

A series RLC circuit has a resonant frequency of 6 kHz. When it is driven at 8 kHz, it has an impedance of 1 k W and a phase constant of 45o. What are R, L, and C for this circuit ?

9

An alternating source drives a series RLC circuit with an emf amplitude of 6 V, and voltage leads current by a phase of + 30o When the potential difference across the capacitor reaches its maximum positive value of +5 V, what is the potential difference across the inductor ( sign included ) ?

10

In the given series LCR circuit, what will be the voltmeter and ammeter readings ?

11

The current amplitude I versus driving angular frequency wd for a driven RLC circuit is as shown in the figure. The inductance is 200 mH, and the emf amplitude is 8 V. What is the capacitance C and resistance R of the circuit ?

12

For the circuit shown in figure, amplitude of the external sinusoidal voltage is Vo Under the action of a constant voltage = twice the amplitude of voltage of source, the capacitor is charged to Qo. Long time after the switch is closed, determine the amplitude of charge on capacitor in steady state oscillations at resonance, in terms of Qo , R , L and C

13

An LCR circuit contains resistance of 100 W and a supply of 200 V at 300 rad/s. If only capacitance is taken out from the circuit and the rest of the circuit is joined, current lags behind the source voltage by 60o. If only inductor is taken out, the current leads by 60o with the source voltage. What will be the current in circuit when both capacitor and inductor are present ?

14

In an RLC series circuit shown in figure, the readings of voltmeters V1 and V2 are 100 V and 120 V, respectively. The source voltage is 130 V. Find the rms voltage across resistor, inductor and capacitor.

15

Figure shows an RLC circuit that contains two identical capacitors and two switches. The emf amplitude is 12 V, and the driving frequency is 60 Hz. With both switches open, the current leads the emf by 30o. With switch S1 closed and switch S2 still open, the emf leads the current by 30o. With both switches closed, the current amplitude is 447 mA. Find the value of R , C and L .

16

A box P and a box Q are connected in series with an ac source of variable frequency. The emf of the source is constant at 10 V. Box P contains a capacitor of 10 mF in series with a resistance of 20 W . Coil Q has an inductance of 4 mH and a resistance of 30 W in series. Frequency of source is adjusted so that maximum current flows in P and Q. a) The impedance of P at this frequency is b) The impedance of Q at this frequency is c) The voltage across P is d) The voltage across Q is

17

A circuit consists of a resistor, an inductor and a capacitor in series connected to the mains. Varying the capacitance of the capacitor, the heat power generated in the circuit was increased ? times. How much (in percent) was the value of cos f changed in the process ?

18

A series LCR circuit containing a resistance of 120 W has angular resonance frequency 4 x 105 rad s-1. At resonance the voltages across resistance and inductance are 60 V and 40 V, respectively. What is the voltage of source ? What is the value of inductance ? What is the value of capacitance ? What is the power factor and power delivered by source ?

19

a) When a voltage vs = 100 2 sin ( wt + 15o ) V is applied to a circuit, the current in the circuit is found to be i = 2 2 sin [ wt + ( p/4 ) ] A. Find the average power consumed in the circuit. b) A voltage with amplitude = 110 V is applied across a series circuit having a resistance 11 W and a net reactance 11 W. Power consumed in circuit will be ?

20

A bulb is rated at 100 V, 100 W. It can be treated as a resistor. Find out the inductance of an inductor (called choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an ac source of 200 V and 50 Hz.

21

An ideal choke coil is needed to operate a bulb at 130 V (rms) and 100 rad/s. Bulb has an effective resistance of 5 W when running on 10 A (rms). Calculate the inductance of the choke coil. If the same bulb is to be operated on 130 V (dc), what additional resistance is required ? Compare the power losses in both the cases.

22

A series RLC Circuit, driven with Erms = 120 V at frequency fd = 60 Hz, contains a resistance R = 60 W, an inductance with XL = 80 W, and a capacitance with Xc = 160 W. a) What is the power factor and power factor angle of the circuit ? b) What is the average power dissipated in the resistor ? c) If the capacitor is to be replaced with a new capacitor, such that power dissipated in the circuit is maximum, what should be the value of new capacitance ?

23

A coil with inductance L and active resistance r is connected in series with an inductance-free resistance R. An alternating voltage with amplitude V and frequency w is applied across the terminals of this circuit. At what value of the resistance R will the maximum heat power be generated in the circuit? What will be the phase between voltage and current at maximum power ? What will be the wattless current at maximum power ?

24

In figure a square loop consisting of an inductor of inductance L and resistor of resistance R is placed between two long parallel wires. The two long straight wires have time ? varying current of magnitude I = Io cos wt but the directions of current in them are opposite. Find the equation of instantaneous current in the circuit.

25

A thin conducting ring with active resistance R and inductance L rotates with constant angular velocity w in the external uniform magnetic field perpendicular to the rotation axis. In the process, the flux fo magnetic induction of external field across the ring varies with time as f = fo cos wt. Find a) the peak value of current in ring. b) the equation of current in the ring as a function of time c) the mean mechanical power developed by external forces to maintain the constant angular speed of rotation of ring

26

An AC current is given by equation i (t) = I1 cos wt + I2 sin wt. RMS value of current will be

27

Find the effective value of current i3 in the circuit shown below.

28

A capacitor with capacitance C and a coil with active resistance R and inductance L are connected in parallel to an AC source with peak voltage Vo and angular frequency w. Find the a) amplitude of current through capacitor and coil b) amplitude of current supplied by source c) phase difference between the current and the source voltage d) resonance angular frequency of circuit e) impedance of circuit at resonance

29

For the circuit shown in figure, find the amplitude of current through source and phase angle, in terms of the resistance R, capacitive reactance XC, inductive reactance XL and amplitude of source voltage Vo

30

In the circuit shown in figure, find a) amplitude of current through R-L and R-C section b) phase difference between current and voltage through R-L and R-C section c) amplitude of current through source and phase between current and voltage of source d) what must be the relation between RL and RC for the circuit to be resonant at all frequencies ?

31

In the given circuit, the ac source has w = 100 rad/s. Find : a) Amplitude of current through source b) Phase difference between the source voltage and current c) Amplitude and RMS voltage across both resistors

32

For the circuit shown in figure, find the necessary condition for which the phase difference between the current and voltage is zero at all frequencies.

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