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  4. In the circuit given E=6.0 V , R1=100 Ω, R2=R3=50 Ω, R4=75 Ω. The equivalent resistance of the circuit, in ohms, is

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Q. In the circuit given $E=6.0 \,V , R_{1}=100 \,\Omega, R_{2}=R_{3}=50\, \Omega$, $R_{4}=75 \,\Omega$. The equivalent resistance of the circuit, in ohms, isPhysics Question Image

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Solution:

In given circuit three resistance $R_{2}, R_{4}$ and $R_{3}$ are parallel.
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$\frac{1}{R}=\frac{1}{R_{2}}+\frac{1}{R_{4}}+\frac{1}{R_{3}}$
$=\frac{1}{50}+\frac{1}{50}+\frac{1}{75}$
$=\frac{75+75+50}{50 \times 75}$
$R=\frac{50 \times 75}{75+75+50}$
$=\frac{50 \times 75}{200}=\frac{75}{4} \Omega$
$=18.75 \,\Omega$
This resistance is in series with $R_{1}$.
$\therefore R_{\text {resultant }}=R_{1}+R=100+18.75$
$=118.75\, \Omega$