The emf of a cell having internal resistance 1 is balanced against a length of 330 ~cm on a potentiometer wire. When an external resistance of 2 is connected across the cell, the balancing length will be

Correct answer: C. 220 ~cm For case - I aligned & _s=φ × 330 & φ=( _s)/(330)( V cm ) aligned For case - II aligned & i × 2=φ I_2 & ( _s)/(3) × 2=( _s)/(330) × I_2 [From equation 1] & I_2=220 cm aligned

NEET 2023

Exam: NEET
Year: 2023
Subject: Physics
Chapter: Current Electricity

NEET 2023 · Physics · Current Electricity

The emf of a cell having internal resistance 1 is balanced against...

The emf of a cell having internal resistance

1 \Omega

is balanced against a length of

330 \mathrm{~cm}

on a potentiometer wire. When an external resistance of

2 \Omega

is connected across the cell, the balancing length will be

Options

A $115 \mathrm{~cm}$
B $332 \mathrm{~cm}$
C $220 \mathrm{~cm}$
D $330 \mathrm{~cm}$

Correct answer

C. $220 \mathrm{~cm}$

Step-by-step solution

For case - I

\begin{aligned} & \Rightarrow \varepsilon_s=\phi \times 330 \\ & \Rightarrow \phi=\frac{\varepsilon_s}{330}\left(\frac{V}{\mathrm{ cm}}\right) \ldots\end{aligned}

For case - II

\begin{aligned} & \Rightarrow i \times 2=\phi I_2 \\ & \Rightarrow \frac{\varepsilon_s}{3} \times 2=\frac{\varepsilon_s}{330} \times I_2 \text{ [From equation 1] } \\ & \Rightarrow I_2=220 \mathrm{ cm}\end{aligned}

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