A $10\,\text{m}$ long potentiometer wire of uniform cross-section and $20\,\Omega$ resistance is connected in series with a $5\,\text{V}$ battery and an external resistance of $480\,\Omega$. An unknown EMF $E$ is balanced at a length of $6.0\,\text{m}$. Calculate (i) the potential gradient and (ii) the value of the unknown EMF.

(i) Potential gradient $k=0.02\,\text{V m}^{-1}$. \; (ii) $E=0.12\,\text{V}$.

CBSE Class 12 · 2006 · Current ElectricityShort Answer

10 m

long potentiometer wire of uniform cross-section and

20 Ω

resistance is connected in series with a

5 V

battery and an external resistance of

480 Ω

. An unknown EMF

E

is balanced at a length of

6.0 m

. Calculate
(i) the potential gradient and
(ii) the value of the unknown EMF.

Answer: (i) Potential gradient $k = 0.02 V m^{- 1}$ . \;
(ii) $E = 0.12 V$ .

Current in the wire

I = \frac{V}{R _{A B} + R} = \frac{5}{20 + 480} = 0.01 A

. Potential drop across the

10 m

wire

= I R_{A B} = 0.01 \times 20 = 0.2 V

. (i)

k = \frac{0.2}{10} = 0.02 V m^{- 1}

. (ii)

E = k ℓ = 0.02 \times 6 = 0.12 V .

CBSE Class 12 Board · 2006 · Subjective