Question

10 m long uniform wire of resistance 2Ω per metre is connected in series with a battery of emf 3 V and a resistance 10Ω. The potential gradient along the wire (in V/m) is ______.

Options

• 0.1

• 1

• 2

• 0.2

Answer 1

10 m long uniform wire of resistance 2Ω per metre is connected in series with a battery of emf 3 V and a resistance 10Ω. The potential gradient along the wire (in V/m) is 0.2.

Explanation:

Given, l = 10 m, `R/l = 2` Ω/m

⇒ R = 2l = 2 × 10 = 20Ω

Emf of the cell, ε = 3 V

Series resistance, R_s = 10Ω

Potential across wire, V = lR = `(ε xx R)/(R + R_s)`

= `(3 xx 20)/((20 + 10)) = 2V`

Potential gradient, K = `V/l = 2/10 = 0.2` V/m