Question

09. Two wires A and B are of equal length and have equal resistance. If the resistivity of A
is more than that of B which wire is thicker and why? For the electric circuit given
below calculate:
mi
(i) Current in each resistor,
(ii) Total current drawn from the battery, and
(iii) Equivalent resistance of the Circuit​

Answer 1

Using, R = ρ l/A

ρ/A = R/l = Constant = K(for same l and R)

ρ = kA

ρ ∝ A

So, for different materials having same resistance per unit length, greater resistivity material wire has more cross-sectional area.

Hence, wire A is thicker than that of B.

(i) Current through each resistor

I1 = V/R1 = 6/5 = 1.2 A

I2 = V/R2 = 6/10 = 0.6 A

I3 = V/R3 = 6/30 = 0.2 A

Current in 5Ω, 10Ω and 30Ω are therefore, 1.2A, 0.6A and 0.2A respectively.

(ii) Total current drawn from the battery

I = I1 + I2 + I3 = 1.2 + 0.6 + 0.2 = 2.0 A

(iii) R1 = 5Ω, R2 = 10Ω and R3 = 30Ω are connected in parallel. So their equivalent resistance

1/R = 1/R1 + 1/R2 + 1/R3

= 1/5 + 1/10 + 1/30 = 1/3

R = 3Ω