ohms law practice problems

problem 1

A coil consists of 2000 turns of copper wire having a cross-sectional area of 0.8 mm2. The mean length per turn is 80 cm and the resistivity of copper is 0.02 μΩ–m. Find the resistance of the coil and power absorbed by the coil when connected across 110 V d.c. supply.

Solution 1

Length of the coil, l = 0.8 × 2000 = 1600 m ;
A = 0.8 mm2 = 0.8 × 10^−6 m2.
R =  ρ =×(1/A) 0.02 × 10−6 × 1600/0.8 × 10^−6 = 40 Ω 
Power absorbed = V^2 / R = 1102/40 = 302.5 W

problem 2

Example 1.4. An aluminium wire 7.5 m long is connected in a parallel with a copper wire 6 m long. When a current of 5 A is passed through the combination, it is found that the current in the aluminium wire is 3 A. The diameter of the aluminium wire is 1 mm. Determine the diameter of the copper wire. Resistivity of copper is 0.017 μΩ-m ; that of the aluminium is 0.028 μΩ-m.

Solution 2

problem 3

A rectangular carbon block has dimensions 1.0 cm × 1.0 cm × 50 cm. (i) What is the resistance measured between the two square ends ? (ii) between two opposing rectangular faces / Resistivity of carbon at 20°C is 3.5 × 10−5 Ω-m. (b) A current of 5 A exists in a 10-Ω resistance for 4 minutes (i) how many coulombs and (ii) how many electrons pass through any section of the resistor in this time ? Charge of the electron = 1.6 × 10−19 C.

Solution 3

R = ρ l/A
Here, A = 1 × 1 = 1 cm2 = 10−4 m2 ; l = 0.5 m
R = 3.5 × 10−5 × 0.5/10−4 = 0.175 Ω
L= 1 cm; A = 1 × 50 = 50 cm2 = 5 × 10−3 m2
R = 3.5 × 10−5 × 10−2/5 × 10−3 = 7 × 10−5 Ω

Q = It = 5 × (4 × 60) = 1200 C
n = (Q/e)= (1200/(1.6 × 10^-19))= 75 × 10^20