Current Electricity — Practice

Question 1

A wire of resistivity 1.7 x 10^-8 ohm metre has length 2.0 m and cross-section 1.0 x 10^-6 m squared. Find its resistance.

Accepted Answer

Apply R = rho L/A, which combines the material property with the geometry. Answer: R = 0.034 ohm.

Question 2

A cell of emf 1.5 V and internal resistance 0.5 ohm is connected to a 2.5 ohm resistor. Find the current.

Accepted Answer

The emf is shared between external and internal resistance, so I = emf/(R + r). Answer: I = 0.5 A.

Question 3

A battery of emf 6 V drives 1.5 A through an external resistance of 3.5 ohm. Find the internal resistance and terminal voltage.

Accepted Answer

Since emf = I(R + r), solve for r, then use V = emf - I r. Answer: r = 0.5 ohm; V = 5.25 V.

Question 4

A wire has resistance 10 ohm at 20 degrees Celsius and 12 ohm at 120 degrees Celsius. Find alpha.

Accepted Answer

Rearrange R2 = R1[1 + alpha(T2 - T1)] for alpha, taking R1 at the lower reference temperature. Answer: alpha = 2.0 x 10^-3 per degree Celsius.

Question 5

Three resistors of 2, 3 and 6 ohm are connected in parallel across a 12 V supply. Find the total current.

Accepted Answer

Combine reciprocally to get 1 ohm, then apply Ohm's law to the combination. Answer: I = 12 A.

Question 6

Two cells of emf 2 V and 4 V with internal resistances 1 ohm and 2 ohm are connected in parallel across a 4 ohm resistor. Find the current through the resistor.

Accepted Answer

Apply the loop and junction rules to the two-loop network and solve the simultaneous equations. Answer: I = 0.6 A approximately.

Question 7

A copper wire of cross-section 1.0 x 10^-6 m squared carries 1.5 A. If n = 8.5 x 10^28 per cubic metre, find the drift velocity.

Accepted Answer

Rearrange I = nAev_d for the drift velocity and note how small the result is. Answer: v_d = 1.1 x 10^-4 m/s.

Question 8

In a Wheatstone bridge P = 10 ohm, Q = 20 ohm and R = 15 ohm at balance. Find S.

Accepted Answer

At balance no current flows through the galvanometer and P/Q = R/S. Answer: S = 30 ohm.

Practice — Current Electricity

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