Question

Find the equivalent resistance between a and b

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{R_{equivalent} =5 \: ohm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline{\bold{Given:}}} \\ \tt: \implies R_{1} = 6 \: ohm \\ \\ \tt: \implies R_{2} = 3 \: ohm \\ \\ \tt: \implies R_{3} = 4 \: ohm \\ \\ \tt: \implies R_{4} = 12 \: ohm \\ \\ \red{\underline{\bold{To \: Find:}}} \\ \tt: \implies R_{equivalent} =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{1}{R_{34}} = \frac{1}{ R_{3}} + \frac{1}{ R_{4} } \\ \\ \tt: \implies R_{34} = \frac{ R_{3} R_{4} }{ R_{3} + R_{4}} \\ \\ \tt: \implies R_{34} = \frac{4 \times 12}{4 + 12} \\ \\ \green{\tt: \implies R_{34} = 3 \:ohm} \\ \\ \bold{Similarly : } \\ \tt: \implies \frac{1}{R_{12}} = \frac{1}{ R_{1}} + \frac{1}{ R_{1} } \\ \\ \tt: \implies R_{12} = \frac{ R_{1} R_{2} }{ R_{1} + R_{2}} \\ \\ \tt: \implies R_{12} = \frac{6 \times 3}{6+ 3} \\ \\ \green{\tt: \implies R_{12} = 2 \:ohm} \\ \\ \bold{For \: R_{equivalent}} \\ \tt: \implies R_{equivalent} = R_{12} + R_{34} \\ \\ \tt: \implies R_{equivalent} =2 + 3 \\ \\ \green{\tt: \implies R_{equivalent} =5 \: ohm}$