Electric Power

What is Electric Power ? What drives energy in electrical circuits ? How is this energy used up in Resistors and Capacitors ?

Q1

A house is fitted with two fans of 80 W each, four bulbs of 50 W each, one refrigerator of 500 W and an A.C of 2.5 kW (all at the voltage supplied to the house). Calculate the bill for the month if fans are used for 10 hours daily, bulbs are used for 7 hours daily, refrigerator for 24 hours daily and A.C for 6 hours daily. Cost of electricity is Rs. 4/- per unit

Q2

A power transmission line having total resistance of 0.1 W delivers 24 kW at 240 V to a factory. Calculate the efficiency of transmission.

Q3

A real battery of e.m.f. 5 V and internal resistance 0.1 W is connected across a resistor. Current is the resistor is found to be 2 A. a) What is the rate of chemical energy consumption in the cell ? b) What is the rate of energy dissipation inside the cell ? c) What is the rate of heat dissipation in the external resistor ?

Q4

4 cells each of e.m.f 2 V and internal resistance 0.25 W is charged by a 50 V supply. What resistance should be used in the charging circuit in order to limit the charging current to 6 A. Using this relation, obtain a) the power supplied by the d.c source b) the power dissipated as heat c) the power used up in charging the cells

Q5

i) A constant voltage V is applied between the ends of a uniform metal wire of length L and radius R. Some heat is developed in it. The heat developed in the same time is doubled if a) both L and R are halved b) both L and R are doubled c) Area is doubled, keeping L the same d) L is doubled, keeping R the same ii) A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will be a) one fourth b) halved c) doubled d) four times iii) Two electric bulbs have tungsten filament of same length. If one of them gives 100 W and the other 50 W, then a) 100 W bulb has thicker filament b) 50 W bulb has thicker filament c) both filaments are of same thickness d) cannot be concluded

Resistor Combination

Ratio of Power Dissipation in Series and Parallel combination of Resistors

Q6

Three resistances of equal value are connected in four different combinations as shown in figure. Arrange them in increasing order of power dissipation.

Q7

a) There are n identical resistors. First they are connected in series across a potential source and then they are connected in parallel. Find the ratio of power consumed in them in the two cases. b) A wire when connected to 200V mains supply has power dissipation P1. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in the case is P2. Then P2 : P1 is ______ ?

Electric Appliances

What does the Power rating of Electrical appliances mean ? Why is the Power rating specified at a particular voltage ?

Q8

A 100 W bulb is designed to operate on a potential difference of 240 V. a) Find the resistance of the bulb. b) Find the current drawn by the bulb if it operated at a potential difference for which it is designed. c) Find the current drawn and power consumed by the bulb if it is connected to 200 V supply. d) What is the percentage change in power consumed when the voltage is changed from 240 V to 200 V.

Q9

An electric kettle has a rated power of 2 kW. It takes 10 mins to heat 1 kg of water from 20 oC to boiling point. What is the amount of heat that is lost ?

Q10

A motor operating on 240 V draws a current of 2 A. If there is heat developed in the motor at the rate of 50 cal/s, what is its efficiency ? Estimate the resistance of the winding of the motor.

Appliance Combination

What is the Power consumption in each appliance if different appliances with different power ratings are connected in Series/Parallel to a common Voltage source ?

Q11

Two bulbs are marked 60 W, 200 V and 30 W, 200 V. a) Which bulb will be brighter if they are connected in series to a 200 V supply ? b) Which bulb will be brighter if they are connected in parallel to a 200 V supply ? c) Also find the total power consumed by both the bulbs in each of the two cases above. It is given that if the potential difference across the bulbs exceeds the rated voltage then they are fused, d) Which bulb will be fused if they are connected in series to a 200 V supply ? e) Which bulb will be fused if they are connected in parallel to a 200 V supply ?

Q12

There are two heating coils used to boil water. When one of the coils is switched on, boiling begins in 3 min. When the other coil is switched on, boiling begins in 6 min. In what time, will the boiling begin if both coils are switched on simultaneously a) in series b) in parallel

Q13

A 100 W bulb and two 60 W bulbs are connected to a 250 V source, as shown in figure. If P1, P2 and P3 are the output powers of the bulbs B1, B2 and B3 respectively. Then a) P1 > P2 = P3 b) P1 > P2 > P3 c) P1 < P2 = P3 d) P1 < P2 < P3

Q14

Compare the brightness of bulbs in each circuit.

Q15

What happens to the power of each bulb when the given operation is done.

Q16

Two bulbs are marked 200 V, 100 W and 100 V, 100 W respectively. i) The bulbs are connected in series and the combination is connected to a 200 V supply. a) Which bulb will produce more illumination ? b) Find the total power consumed by both the bulbs. ii) The bulbs are connected in parallel and the combination is connected to a 200 V supply. a) Which bulb will produce more illumination ? b) Find the total power consumed by both the bulbs.

Max Power Transfer

In a practical case where the source of voltage also has an internal resistance, what should be value of external resistance so that maximum power is transferred to the external resistor ?

Q17

Three equal resistance, each of R W, are connected as shown in the figure. A battery of 30 volts and internal resistance 3 W is connected across the circuit. Calculate the value of R for which the heat generated in the circuit is maximum.

RC Charging - 1

Derivation of equations for a Charging RC Circuit ? part 1

RC Charging - 2

Derivation of equations for a Charging RC Circuit ? part 2

Q18

Find the time at which charge and current in a charging RC Circuit is a) 10 % b) 50 % c) 90 % d) 99 % of its maximum value

Q19

A charging RC circuit has resistance R and and capacitance C. What will be the change in a) initial current b) final charge on capacitor c) time constant of circuit if : i) Resistance is doubled ii) Capacitance is doubled

RC Discharging

Derivation of equations for a Discharging RC Circuit

Q20

A resistor and a capacitor are connected as shown in the figure. The capacitor is originally charged to a potential of E and then discharged by closing the switch at t = 0. Find the time at which charge on capacitor, potential difference across it and current in the circuit is a) 10 % b) 50 % c) 90 % d) 99 % of its maximum value

Q21

A capacitor, initially charged to potential of Eo, is discharged through a resistor. If the potential across capacitor is V1 at time t1, what is the potential across capacitor at time 2 t1

Q22

Ratio of charge on the capacitor to current in the circuit is a) constant for a charging circuit b) changes with time for a charging circuit c) constant for a discharging circuit d) changes with time for a discharging circuit

Eq. Time Const

Equivalent Time Constant method for simplifying RC circuits

Q23

Figure shows three circuits connected the same battery via a switch. The resistors and capacitors are all identical. Rank the circuits according to a) the final charge on the capacitor b) the time required for the capacitor to reach 50% of the final charge

Q24

In the circuit shown in figure, the battery is ideal with e.m.f. V. The capacitor is initially uncharged. The switch S is closed at time t = 0. a) Find the charge Q on the capacitor at time t. b) Find the current in each resistor at time t and in steady state.

Q25

In the given circuit, the switch S is closed at time t = 0. Find the a) charge on the capacitor, b) potential difference across the capacitor and c) current in each segment as a function of time. If at any instant t, charge on capacitor is given by Q(t) = Q ( 1 ? e-at ). Find the value of Q, and a in terms of given parameters as shown in the circuit in figure

RC Charged Cap

Derivation of equations for a Charging RC circuit with Capacitor being initially charged to some voltage.

RC Energy Charging

Derivation of equations of Energy changes in a charging RC Circuit

RC Energy Discharging

Derivation of equations of Energy changes in a discharging RC Circuit

Q26

In a charging circuit, after how many time constants will the a) energy stored on capacitor b) energy dissipated as heat c) energy supplied by battery reach half of its corresponding maximum value ? In a discharging circuit, after how many time constants will the a) energy stored on capacitor b) energy dissipated as heat reach half of its corresponding maximum value ?

Q27

In a charging RC circuit, find the Energy supplied by battery, Energy dissipated as heat and Energy stored on Capacitor from t = t to t = 2 t.

RC Power

Variation of Electric Power in RC Circuits

Q28

A Capacitor of capacitance C is connected to a resistance R and a battery of e.m.f. E and negligible internal resistance. Find a) Power delivered by the battery b) Power dissipated as heat c) Rate of energy stored in the capacitor at i) t = t ii) t = 2 t d) Find the time at which the respective powers are half of their maximum value.

Q29

For a Charging RC Circuit, 1) When Charge on the capacitor is maximum, then current in circuit is ______ zero/not zero 2) When current in circuit is maximum, charge on capacitor is ______ zero/not zero 3) When power supplied by battery is maximum, then charge on capacitor is ______ zero/not zero 4) When charging rate of capacitor is maximum, current through circuit is ______ zero/not zero 5) When Power transfer to capacitor is maximum, current is ______ zero/not zero 6) The difference in power supplied by battery and power consumed in resistance at t = 0 is ______ zero/not zero

1

Two resistors, each with resistance of R, are connected in series with two batteries, each with emf V. Then the circuit is split such that each resistor is connected across each battery. What is the total power dissipation in each case ?

2

Two wires with same mass, but having ratio of the lengths 2 : 3, density 3 : 5 and resistivity 3 : 1. They are connected to the same voltage supply. Find the ratio of rate of the heat dissipation in them.

3

A water heater taking 2 A at 240 V, brings 500 gms of water from 40 oC to boiling point in 10 mins. Find its efficiency. In order to reduce the time of operation, length of coil should be increased/decreased ?

4

The walls of a closed cubical box of edge 10 cm are made of a material of thickness 1 mm and thermal conductivity 4 x 10-4 / cal-cm-oC. Interior of the box is maintained at 100 oC above the outside temperature by a heater placed inside the box and connected across 200 V d.c. Calculate the resistance of the heater.

5

A wire of length L is connected to 3 identical cell of negligible internal resistance. Due to heat dissipation in wire, temperature of wire is raised by DT in time t. Now N similar cells are connected to a wire of same material and cross section but length 2L. Temperature of wire is raised by the same amount DT in the same time t . Find the value of N.

6

The efficiency of a real cell when connected to a resistance R is 60 %. What will be its efficiency if the external resistance is increased by ten times ?

7

Find the power dissipated in the marked resistor.

8

In the circuit shown in the figure, the rate of heat produced in the 5 W resistor is 20 J s-1. Find the rate of heat produced in the 4 W resistor.

9

An electric bulb with rating of 500 W, 100 V, is used in a circuit having a 200 V supply. What resistance must be connected in series with the bulb so that it delivers 500 W? A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected, in combination with a resistance R, to a 100 V mains as shown in Figure. What should be the value of R such that heater may operate with a power of 500 W?

10

A house is fitted with certain number of 60 W, 240 V bulbs. The power to the house is supplied by a generator producing the power at 300 V. The resistance of the wires from generator to the house is 10 W. Find the maximum number of bulbs that can be illuminated so that voltage across none of the lamps drops below 240 V.

11

A 200 V power supply is connected to a circuit protected by a fuse of 10 A. Maximum number of ( 100 W, 200 V ) bulbs that can be safely connected in parallel to this circuit is ______ ?

12

In the circuit shown in figure, Max allowed power dissipation in each resistor is shown. a) Find the maximum power the circuit can dissipate. b) Find the maximum safe value of E.

13

A battery of internal resistance 4 W is connected to the network of resistances as shown in the figure. In order that maximum power can be delivered to the network, the value of R in ohms should be _____?

14

Two cells, each of e.m.f E and internal resistance r, are connected in parallel across a resistor R. Power delivered to the resistor is maximum if R is _______ ? For this value of R, power delivered to the resistor is _______ ?

15

Charge flowing through a resistance R varies with time t as Q (t) = At - Bt2. Find the time when current in the resistor is zero. Find the total heat produced in R from t = 0 to the time calculated above.

16

A leaky parallel plate capacitor is filled completely with a material having a dielectric constant K = 6 and electrical conductivity s = 6 ? 10-12 W-1m-1. If the charge on the capacitor at instant t = 0 is Q = 8.85 mC, then calculate the leakage current at the instant t = 17.7 s.

17

Variation of voltage across the capacitor is as shown in figure. Plot the varitaion of voltage across the resistor.

18

For the circuit shown in figure, capacitor is charged when the switch is closed and is discharged when the switch is opened. What is the ratio of time constant during charging and discharging of the capacitor ?

19

A part of circuit in steady state is as shown in the figure along with the current flowing in the branches. Find the energy stored in the capacitor.

20

Find the potential difference between the points A and B in the steady state.

21

Find the current through the battery a) Immediately after the switch S is closed b) After a long time

22

Find the charge on the capacitors in steady state

23

a) What is the potential difference between points a and b when switch is open? b) A long time after the switch is closed, what is the change in charge on capacitors ?

24

In the circuit shown in figure, all resistances are equal to R and all capacitors are equal to C. Find a) the current supplied by battery just when the switch is closed and after a long time b) total energy stored on capacitors after a long time c) total heat dissipated in the circuit

25

In the circuit shown in figure, switch S has been closed for a long time. It is opened again at t = 0. Find the time at which charge on capacitor has reduced to 2/3 of its initial charge.

26

In the circuit shown in figure, switch is closed at position 1 for long time. Then the switch is shifted to position 2. Find the total heat generated in resistor of resistance 2R1, after the switch has been in position 2 for a long time.

27

In the circuits shown in figure, after the switch is closed, the ratio i1/i2 is constant True / False

28

Calculate the current in branches containing R1, R2 and R3 in the circuit shown below

29

There is a large container, holding 500 litres of water, lying 2 m above a hydro - generator wheel, which is to be used to light a 40 W bulb. At what rate water must drain out from the container, in order to light the bulb ? For how long will the bulb be lighted ? Given, g = 10 ms-2 and the efficiency of the generator is 80%

30

For the circuit shown in figure, find a) the current through the battery b) potential difference across RL c) ratio of power dissipated in R1 and R2 d) if R1 and R2 are interchanged, find the power dissipated in RL

31

n identical bulbs are connected i) in series ii) in parallel and illuminated by a power supply. When one of the bulbs is removed, find the percentage change in the illumination of a) all the bulbs b) each bulb

32

For the given RC circuit, switch S1 is closed and S2 is open till the capacitor is fully charged. Then S1 is opened and S2 is closed simultaneously till the charge on capacitor remains Q/3, for which it takes time t1. Now S2 is again opened and S1 is closed till charge on capacitor becomes 2Q/3, for which it takes time t2. Find the ratio t1/t2

33

In the circuit shown in figure, the capacitor is a parallel-plate air capacitor with plate area A = 100 cm2 and distance d = 1 mm apart. Two identical ideal batteries with e.m.f. E are connected as shown in figure. If a dielectric strength of air is Ea = 3 x 106 Vm-1, calculate the maximum safe value of E.

34

In the circuit shown in figure, find a) current supplied by the battery, just when the switch is closed and in steady state b) charge stored in the capacitors in steady state

35

The capacitor shown in fig. has been charged to a potential difference of V volt so that it carries a charge CV with both the switches S1 and S2 remaining open. Switch S1 is closed at t = 0. At t = R1 C, switch S1 is opened and S2 is closed. Find the charge on the capacitor at t = 2R1 C + R2 C.

36

In the given circuit, resistances are in ohms. Find the energy stored in the capacitor.

37

A capacitor of capacitance C is initially charged to a potential of V. It is then connected to an uncharged capacitor of equal capacitance C through a resistance R. Find the charge on capacitors as a function of time. What is the total heat dissipated in the circuit ?

38

For the circuit arrangement shown in figure a) Find the current supplied by battery just when the switch is closed. b) Find the charge on capacitor and current through it, at time t after the switch is closed. Also find the current supplied by battery at time t. c) What is the charge on each capacitor and current supplied by battery in steady state. d) After a long time, the switch is opened again. Find the current in the 6 W resistor at time t after the switch is opened again.

39

Consider the network shown in figure. Initially, the switch S1 is closed and S2 is open a) Calculate VA - VB b) When S2 is also closed, what is VA - VB i) just after closing ii) after long time c) Find the expression of charge on capacitor and current through it as a function of time.

40

Find the potential difference between the points a and b, a) just when the switch is closed b) in steady state c) as a function of time

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