Current Electricity - Result Question 42

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44. A current of 2 A flows through a $2 \Omega$ resistor when connected across a battery. The same battery supplies a current of $0.5 A$ when connected across a $9 \Omega$ resistor. The internal resistance of the battery is

======= ####44. A current of 2 A flows through a $2 \Omega$ resistor when connected across a battery. The same battery supplies a current of $0.5 A$ when connected across a $9 \Omega$ resistor. The internal resistance of the battery is

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/current-electricity/current-electricity—result-question-42.md (a) $0.5 \Omega$

(b) $1 / 3 \Omega$

(c) $1 / 4 \Omega$

(d) $1 \Omega$

[2011]

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Answer:

Correct Answer: 44. (b)

Solution:

  1. (b) Let the internal resistance of the battery be $r$. Then the current flowing through the circuit is given by

$i=\frac{E}{R+r}$

In first case,

$2=\frac{E}{2+r}$

In second case,

$0.5=\frac{E}{9+r}$

From (1) & (2),

$4+2 r=4.5+0.5 r$

$\Rightarrow 1.5 r=0.5 \Rightarrow r=\frac{1}{3} \Omega$.

If $I_1$ be the current in a circuit with an external resistance $R_1$ and $I_2$ be the current in the circuit with external resistance $R$, then internal resistance of cell can be find using

$r=\frac{I_2 R_2-I_1 R_1}{I_1-I_2}$