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High School Physics : Calculating Total Resistance

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Example Questions

Example Question #1 : Calculating Total Resistance

Ten resistors, each with $300\Omega$ resistance, are set up in series. What is their equivalent resistance?

Possible Answers:

$30\Omega$

$3\Omega$

$300\Omega$

$30,000\Omega$

$3,000\Omega$

Correct answer:

$3,000\Omega$

Explanation:

For resistors aligned in series, the equivalent resistance is the sum of the individual resistances.

$R_{eq}=R_1+R_2+R_3...$

Since all the resistors in this problem are equal, we can simplify with multiplication.

$R_{eq}=10 (300\Omega)$

$R_{eq}=3000\Omega$

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Example Question #2 : Calculating Total Resistance

Ten resistors, each with $300\Omega$ resistance, are set up in parallel. What is the equivalent resistance?

Possible Answers:

$300\Omega$

$30,000\Omega$

$30\Omega$

$3,000\Omega$

$3\Omega$

Correct answer:

$30\Omega$

Explanation:

For resistors in parallel, the equivalent resistance can be found by summing the reciprocals of the individual resistances, then taking the reciprocal of the resultant sum.

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}...$

Since all the resistors in this problem are equal, we can simplify by multiplying.

$\frac{1}{R_{eq}}=10( \frac{1}{300\Omega})$

$\frac{1}{R_{eq}}=\frac{10}{300\Omega}$

$\frac{1}{R_{eq}}=\frac{1}{30\Omega}$

$R_{eq}=30\Omega$

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Example Question #3 : Calculating Total Resistance

Twelve resistors of equal resistance are set up in series. If the total resistance is $600\Omega$ , what is the resistance of each resistor?

Possible Answers:

$588\Omega$

$50\Omega$

$0.2\Omega$

$5\Omega$

$500\Omega$

Correct answer:

$50\Omega$

Explanation:

The total resistance of resistors in series is the sum of the individual resistances.

$R_{eq}=R_1+R_2+R_3...$

In this case, we know the total resistance and the number of resistors, and we are told that all resistors are of equal strength. That means we can simplify this problem using multiplication.

$R_{eq}=12R_$

We can use the total resistance to solve for the individual value.

$600\Omega=12R$

$\frac{600\Omega}{12}=R$

$50\Omega=R$

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Example Question #4 : Calculating Total Resistance

Three resistors are in a series. They have $10\Omega$ , $18.3\Omega$ , and $21.22\Omega$ of resistance respectively. What is the total resistance?

Possible Answers:

$0.61\Omega$

$0.20\Omega$

$1.43\Omega$

$49.52\Omega$

$16.51\Omega$

Correct answer:

$49.52\Omega$

Explanation:

When working in a series, the total resistance is the sum of the individual resistances.

$R_{eq}=R_1+R_2+R_3...$

Use the given values for each individual resistor to solve for the total resistance.

$R_{eq}=10\Omega+18.3\Omega+21.22\Omega$

$R_{eq}=49.52\Omega$

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Example Question #5 : Calculating Total Resistance

Six resistors are arranged in a series. Their resistances are $32.4\Omega$ , $8.7\Omega$ , $0.77\Omega$ , $65.2\Omega$ , $10\Omega$ , and $26.33\Omega$ . What is their total resistance?

Possible Answers:

$0.04\Omega$

$143.4\Omega$

$23.9\Omega$

$43.4\Omega$

$0.07\Omega$

Correct answer:

$143.4\Omega$

Explanation:

When working in a series, the total resistance is the sum of the individual resistances.

$R_{eq}=R_1+R_2+R_3...$

Use the given values for each individual resistor to solve for the total resistance.

$R_{eq}=32.4\Omega + 8.7\Omega +0.77\Omega + 65.2\Omega + 10\Omega + 26.33\Omega$

$R_{eq}=143.4\Omega$

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Example Question #6 : Calculating Total Resistance

Three resistors are in a parallel circuit. They have resistances of $10\Omega$ , $18.3\Omega$ , and $21.22\Omega$ , respectively. What is their total resistance?

Possible Answers:

$1.86\Omega$

$0.202\Omega$

$4.96\Omega$

$49.52\Omega$

$0.07\Omega$

Correct answer:

$4.96\Omega$

Explanation:

The formula for resistors in parallel is:

$\frac{1}{R_{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}...$

Using the given individual resistances, we can find the total resistance of the circuit.

$\frac{1}{R_{eq}}}=\frac{1}{10\Omega}+\frac{1}{18.3\Omega}+\frac{1}{21.22\Omega}$

$\frac{1}{R_{eq}}}=0.2017\Omega$

$R_{eq}=4.96\Omega$

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Example Question #2 : Calculating Total Resistance

Two resistors in series have $1.8\Omega$ and $32.4\Omega$ resistance, respectively. What is the total resistance?

Possible Answers:

$30.6\Omega$

$0.586\Omega$

$1.71\Omega$

$34.2\Omega$

$0.029\Omega$

Correct answer:

$34.2\Omega$

Explanation:

For resistors in a series, total resistance is equal to the sum of each individual resistance.

$R_{eq}=R_1+R_2+R_3...$

We can use the individual resistances from the question to solve for the total resistance.

$R_{eq}=1.8\Omega+32.4\Omega$

$R_{eq}=34.2\Omega$

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Example Question #7 : Calculating Total Resistance

What is the total resistance of a series circuit with resistors of $2\Omega$ , $0.55\Omega$ , and $4\Omega$ ?

Possible Answers:

$2.57\Omega$

$0.153\Omega$

$2.18\Omega$

$0.389\Omega$

$6.55\Omega$

Correct answer:

$6.55\Omega$

Explanation:

For a series circuit, the formula for total resistance is:

$R_{eq}=R_1+R_1+R_3...$

We are given the values of each resistance, allowing us to sum them to find the total resistance in the circuit.

$R_{eq}=2\Omega+0.55\Omega+4\Omega$

$R_{eq}=6.55\Omega$

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Example Question #1 : Calculating Total Resistance

What is the total resistance of a parallel circuit with resistors of $2\Omega$ , $0.55\Omega$ , and $4\Omega$ ?

Possible Answers:

$0.389\Omega$

$0.458\Omega$

$0.153\Omega$

$2.57\Omega$

$6.55\Omega$

Correct answer:

$0.389\Omega$

Explanation:

The formula for resistance in parallel is:

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}...$

We are given the values for each individual resistor, allowing us to solve for the total resistance.

$\frac{1}{R_{eq}}=\frac{1}{2\Omega}+\frac{1}{0.55\Omega}+\frac{1}{4\Omega}$

$\frac{1}{R_{eq}}=\frac{113}{44}\Omega$

$R_{eq}=\frac{44}{113}\Omega=0.389\Omega$

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Example Question #8 : Calculating Total Resistance

Calculate the resistance of a copper wire with cross-sectional area of $\small 0.501cm^2$ and length of $\small 2m$ .

$\small rho_{Cu}=1.68*10^{-3}\Omega m$

Possible Answers:

$10\Omega$

$53.4\Omega$

$100\Omega$

$13.7\Omega$

$67.1\Omega$

Correct answer:

$67.1\Omega$

Explanation:

The resistance of a wire is given by the following equation:

$R=\rho\frac{L}{A}$

We are given the resistivity ( $\small \rho$ ), cross-sectional area, and length. Using these values, we can solve for the resistance.

First, convert the cross-sectional area to square-meters.

$0.501cm^2*\frac{1m^2}{10000cm^2}=5.01*10^{-5}m^2$

Use the resistance equation to solve.

$R=(1.68*10^{-3}\Omega m)\frac{2m}{5.01*10^{-5}m^2}$

$R=67.1\Omega$

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High School Physics : Calculating Total Resistance

Study concepts, example questions & explanations for High School Physics

All High School Physics Resources

Example Questions

Example Question #1 : Calculating Total Resistance

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Example Question #4 : Calculating Total Resistance

Example Question #5 : Calculating Total Resistance

Example Question #6 : Calculating Total Resistance

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