# Numerical Problems : Current Electricity

#### LEVEL – II

Q:1. A battery of emf 1.4 V and internal resistance 2Ω is connected to a 100 Ω resistor through an ammeter. The resistance of the ammeter is 4/3 Ω . A voltmeter is also connected to find the potential difference across the resistor.
(i) Draw the circuit diagram.
(ii) The ammeter reads 0.02 A. What is the resistance of the voltmeter?
(iii The voltmeter reads 1.10 V. What is the error in reading?

Ans: 200 ohm, 0.23 V

Q:2. Calculate the potential difference between the points A and B between the points B and C of figure in steady state.

Ans: 25 V, 75 V
Q:3. Find the equivalent resistance of the circuits shown in figure between the points a and b. Each resistor has a resistance r.

Ans: r/2 , 4r/5
Q:4. In network shown in figure below calculate potential difference between A and B.

Ans: – 0.5 V
Q:5. In the network of resistors each of resistance R as shown in the figure, calculate the equivalent resistance between the junctions A and E.

Ans: 7R/12
Q:6. (a) In the shown circuit all the resistors are of same resistance R = 11Ω and C = 2μF. They are connected through a battery of 10 V. When cell is switched on, find
(i) maximum current in the circuit
(ii) energy stored in capacitor after time t.

Ans: (i)0.666 A (ii)$\displaystyle \frac{1}{2}CV^2 (1-e^{-t/RC})^2$

Q:7. In the given circuit (see fig.), E1 = 3 volts, E2 = 2 volts, E3 = 6 volts, R1 = 6Ω, R2 = 2Ω R3 = 4Ω, R4= 3Ω and C = 5μF. Find the current in R3 and energy stored in the capacitor at steady state.

Ans: 1.5 A, 14.4 × 10-6 J
Q:8. Find how the voltage across the capacitor C varies with time t (figure) after the shorting of the switch S at the moment t = 0

Ans: $\displaystyle \frac{E}{2}(1-e^{-2t/RC})$

Q:9. In the circuit shown in figure, a voltmeter reads 30 V when it is connected across 400 Ω resistance. Calculate what the same voltmeter will read when it is connected across the 300 Ω resistance.

Ans: 22.4 V

Q:10. An ammeter and a voltmeter are connected in series to a battery with emf E = 6.0 V. When a certain resistance is connected in parallel with the voltmeter, the reading of the latter decreases η = 2.0 times, whereas the reading of the ammeter increases by the same factor. Find the voltmeter reading after the connection of the resistance.

Ans: 2 V

Q:11. Three equal resistances each of R ohm are connected as shown in figure. A battery of 2 V and internal resistance 0.1 Ω is connected across the circuit. Calculate the value of R for which the heat generated in the circuit is maximum.

Ans: 0.3 ohm
Q:12. Find the current flowing through the resistance R1 of the circuit shown in figure if the resistances are equal to R1 = 10Ω. R2 = 20Ω and R3 = 30Ω and the potentials of the points 1, 2, and 3 are equal to φ1 = 10V, φ2 = 6V and φ3 = 5V.

Ans: 0.202 A
Q:13. Find a potential difference φA – φB between the plates of a capacitor C in the circuit shown in figure. If the sources have emf’s E1 = 4.0 V and E2 = 1.0 V and the resistances are equal to R1 = 10Ω, R2 = 20Ω, and R3 = 30Ω. The internal resistances of the sources are negligible

Ans: – 1V
Q: 14. A constant voltage V = 25 V is maintained between points A and B of the circuit (figure). Find the magnitude and direction of the current flowing through the segment CD if the resistances are equal to R1 = 1.0 Ω, R2 = 2.0 Ω, R3 = 3.0Ω and R4 = 4.0 Ω

Ans: 1 A
Q:15. Consider an “alternator chain” shown below

Find the equivalent resistance between A and B.

Ans: (√5  + 1)R

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