Resistance of the circuit

Four resistances of 16 ohms each are connected in parallel. Four such combinations are connected in series. What is the total resistance of the circuit?

64 4 16 8

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1 solution

Mahdi Raza
Jun 30, 2020

For 4 parallel resistors have equivalent resistance of:

1 R p = 1 16 Ω + 1 16 Ω + 1 16 Ω + 1 16 Ω = 4 16 Ω R p = 4 Ω \begin{aligned} \dfrac{1}{R_{p}} &= \dfrac{1}{16} \Omega + \dfrac{1}{16} \Omega + \dfrac{1}{16}\Omega + \dfrac{1}{16}\Omega \\ &= \dfrac{4}{16}\Omega \\ \\ \implies R_{p} &= 4\Omega \end{aligned}

There are 4 such combinations in series. Thus total resistance would be:

\[\begin{align} R &= 4 \times R_{p} \\ R &= 4 \times 4 \Omega \\ R &= \boxed{16 \Omega}

\end{align}\]

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