Circuits

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GRE Subject Test: Physics › Circuits

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What is the total resistance of a circuit containing four resistors ( $5\Omega, 10\Omega, 15\Omega, 20\Omega$ ) hooked up in series.

$50\Omega$

CORRECT

$20\Omega$

$\frac{1}{20}\Omega$

$\frac{1}{50}\Omega$

$\frac{12}{5}\Omega$

Explanation

For a circuit in series, the total resistance is simply given by the sum of each individual resistor:

$R_{Total}=R_1+R_2+R_3+...R_n$

$R_{Total}=5\Omega+10\Omega+15\Omega+20\Omega=50\Omega.$

What is the total resistance of a circuit consisting of three resistors in a parallel configuration? The resistors have the following resistance: $R_1=10\Omega, R_2=20\Omega, R_3=30\Omega.$

$\frac{60}{11}\Omega$

CORRECT

$60\Omega$

$\frac{11}{60}\Omega$

Cannot be determined.

$\frac{1}{60}\Omega$

Explanation

The total resistance of a circuit in parallel is given by the following equation:

$\frac{1}{R_{Total}}=\frac{1}R_{1}+\frac{1}{R_2}+\frac{1}{R_3}$

Now, we just plug in the values, and solve for the total resistance by inverting!

$\frac{1}{R_{Total}}=\frac{1}{10}+\frac{1}{20}+\frac{1}{30}$

$R_{Total}=\frac{1}{\frac{11}{60}}=\frac{60}{11}\Omega$

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