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Two resistors having resistance 8 Ω and 12 Ω are connected in parallel. Find their equivalent resistance.

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Answer

In parallel, if the equivalent resistance is RP, then

1RP=1R1+1R21RP=18+1121RP=3+2241RP=524RP=245⇒RP=4.8Ω\dfrac{1}{RP} = \dfrac{1}{R1} + \dfrac{1}{R2} \\[0.5em] \dfrac{1}{RP} = \dfrac{1}{8} + \dfrac{1}{12} \\[0.5em] \dfrac{1}{RP} = \dfrac{3 +2}{24} \\[0.5em] \dfrac{1}{RP} = \dfrac{5}{24} \\[0.5em] RP = \dfrac{24}{5} \\[0.5em] \Rightarrow RP = 4.8 Ω

Hence, equivalent resistance = 4.8 Ω

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