In the circuit given $E = 6.0 \,V, R_1 = 100\, ohms, R_2 = R_3 = 50\, ohms, R_4 = 75\, ohms$. The equivalent resistance of the circuit, in $ohms$, is
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(c) In given circuit three resistance ${R_2},{R_4}$ and ${R_3}$ are parallel.
$\frac{1}{R} = \frac{1}{{{R_2}}} + \frac{1}{{{R_4}}} + \frac{1}{{{R_3}}}$
$ = \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 ${R_1}$
${R_{{\rm{resultant}}}} = {R_1} + R = 100 + 18.75 = 118.75\,\Omega $
$\frac{1}{R} = \frac{1}{{{R_2}}} + \frac{1}{{{R_4}}} + \frac{1}{{{R_3}}}$
$ = \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 ${R_1}$
${R_{{\rm{resultant}}}} = {R_1} + R = 100 + 18.75 = 118.75\,\Omega $
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