Eight resistors of 10000 Ω 10000 \ \Omega in series provide the same resistance as eight resistors of x Ω x \ \Omega in parallel. Find x x .

80000 8000 10000 64000 640000 1000 1250

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2 solutions

Viki Zeta
Aug 16, 2016

Efficient resistance of resistors in series is given by R s = R 1 + R 2 + R 3 + + R n R s = 10000 + 10000 + 10000 + 10000 + 10000 + 10000 + 10000 + 10000 = 8 × 10000 = 80000 1 R p = 1 R 1 + 1 R 2 + + 1 R n 1 R p = 8 R R p = R 8 R s = R p 80000 = R 8 R = 80000 × 8 = 640000 \text{Efficient resistance of resistors in series is given by}\\ R_s = R_1+R_2+R_3+\ldots+R_n \\ \therefore R_s = 10000+10000+10000+10000+10000+10000+10000+10000=8\times10000=80000 \\ \dfrac{1}{R_p} = \dfrac{1}{R_1}+\dfrac{1}{R_2}+\ldots+\dfrac{1}{R_n}\\ \therefore \dfrac{1}{R_p} = \dfrac{8}{R} \\ R_p = \dfrac{R}{8}\\ R_s=R_p\\ 80000=\dfrac{R}{8}\\ R = 80000\times 8=640000

Matt Mcc
Aug 19, 2016

When resistors are in a series their resistance is compounded onto each other as the current must travel through each resistor in succession. So 8 resistors of 10k ohms is 80k ohms.

When resistors are parallel their resistance is split between each other as the current will split up and travel through each resistor individually. So 8 identical resistors of unknown ohms parallel to each other is x/8 ohms.

80,000= x 8 \frac{x}{8}

x=8(80,000)

x=64,000.

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