Consider the circuits shown in the figure. Both the circuits are … - Vidyadip

MCQ

Consider the circuits shown in the figure. Both the circuits are taking same current from battery but current through $R$ in the second circuit is $\frac{1}{10}$ th of current through $R$ in the first circuit. If $R$ is $11 \Omega$, the value of $R$

✓
$9.9 \Omega$
B
$11 \Omega$
C
$8.8 \Omega$
D
$7.7 \Omega$

✓

Answer

Correct option: A.

$9.9 \Omega$

In figure (b) current through $R_2=i-\frac{i}{10}=\frac{9 i}{10}$
Potential difference across $R_2=$ Potential difference across $R$
$\Rightarrow R_2 \times \frac{9}{10} i=R \times \frac{i}{10} \text { i.e. } R_2=\frac{R}{9}=\frac{11}{9} \Omega$
$R_{e q}=\frac{R_2 \times R}{\left(R_2+R\right)}=\frac{\frac{11}{9} \times \frac{11}{1}}{\frac{11}{9}+\frac{11}{1}}=\frac{11}{10} \Omega$
$\text { Total circuit resistance }=\frac{11}{10}+R_1=R=11 \Rightarrow R_1=9.9 \Omega$

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