# Numerical Problems : Current Electricity

#### LEVEL – I

Q:1. A wire of resistance 15 Ω is bent to form a regular hexagon ABCDEFA.
Find the equivalent resistance of the loop between the points
(a) A and B, (b) A and C and (c) A and D.

Ans: (a) 2.08 Ω , (b) 3.33 Ω, (c) 3.75 Ω

Q:2. Find the potential difference Va – Vb in the circuits shown in figure

Ans: $\displaystyle \frac{E_1/R_1 + E_2/R_2}{1/R_1 + 1/R_2 + 1/R_3}$

Q:3. Find the P.D. between points A and B in the branch of a circuit shown in figure. Which point is at higher potential

Ans:(i) VA – VB = 12 volt (ii) A

Q:4. In the circuit shown in figure
V1 and V2 are two voltmeters having resistances 6000Ω and 4000Ω respectively E.M.F. of the battery is 250 volts, having negligible internal resistance. Two resistances R1 and R2 are 4000Ω and 6000Ω respectively.

Find the reading of the voltmeters V1 and V2 when
(i) Switch S is open
(ii) Switch S is closed

Ans: (i) 150 V, 100 V (ii) 125 V, 125 V

Q:5. A galvanometer of resistance 95 Ω, shunted by a resistance of 50 ohm gives a deflection of 50 divisions when joined in series with a resistance of 20 kΩ and a 2 volt battery, what is the current sensitivity of galvanometer (in div/µA) ?

Ans: $\displaystyle \frac{1}{2}$ div/µA

Q:6. A part of a circuit in steady state along with current flowing in the branches, with value of each resistance is shown in figure. Calculate the energy stored in the capacitor C.

Ans: 1.8 x 10-3 J

Q:7. Calculate the current through 3 Ω resistor and the power dissipated in the entire circuit shown in figure. The emf of the battery is 1.8 V and its internal resistance is 2/3 Ω

Ans: 0.4 A, 1.62 W

Q:8. A capacitor of capacitance 10 µF is connected to a battery of emf 2 V. It is found that it takes 50 ms for the charge on the capacitor to become 12.6 µC. Find the resistance of the circuit.

Ans: 5 kΩ

Q:9. Three 60 W 120 V light bulbs are connected across a 120 V power line shown in figure. Find (a) the voltage across each bulbs (b) the total power dissipated in the three bulbs.

Ans: (a) 80 V, 40 V, 40 V, (b) 40 W

Q:10. A heater is designed to operate with a power of 1000 watts in a 100 volt line. It is connected in combination with a resistance R, to a 100 volt mains as shown in figure what should be the value of R so that the heater may operate with a power of 62.5 watts.

Ans: 5 Ω

Q:11. Two resistors 400 ohm and 800 ohm are connected in series with a 6V battery. It is desired to measure the current in the circuit. An ammeter of10 ohm resistance is used for this purpose. What will be the reading in the ammeter? Similarly if a voltmeter of 10, 000 ohm resistance is used to measure the potential difference across 400 ohm, what will be the reading of the voltmeter?

Ans: 4.96 mA , 1.95 V

Q:12. Two cells, having emf. of 10 V and 8V respectively, are connected in series with a resistance of 24 Ω in the external circuit.
If the internal resistances of each of these cells in ohm are 200% of the value of their emf respectively, find the current in the circuit.

Ans: 0.3 A

Q:13. A galvanometer having 50 divisions provided with a variable shunt S is used to measure the current when connected in series with a resistance of 90Ω and a battery of internal resistance 10Ω. It is observed that when the shunt resistances are 10Ω and 50Ω respectively, the deflection are respectively 9 and 30 divisions. What is the resistance of the galvanometer ?

Ans: 233 Ω

Q:14. Find the current flowing through the branch AC in the steady state as also the charge on the capacitor C. If the externally applied potential are now withdrawn, how will the charge on the capacitor vary as a function of time? (R = 1 k Ω, C = 10 µF)

Ans: 5 mA, 50 µC, q(t) = 50 µC × e-t/6.67ms

Q:15. In the circuit shown in figure, R1 = 1Ω, R2 = 2Ω, C1 = 1µF, C2 = 2µF and E = 6V. Calculate charge on each capacitor in steady state.

Ans: q1 = 2 mC , q2 = 12 mC

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