AP Physics C Electricity : Calculating Resistance

Study concepts, example questions & explanations for AP Physics C Electricity

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Example Questions

Example Question #1 : Resistors

Three resistors and a battery form the following circuit.

Circuit_1

Calculate the equivalent resistance if the resistors have the following values.

\displaystyle R_1=40\Omega

\displaystyle R_2=25\Omega

\displaystyle R_3=38\Omega

Possible Answers:

\displaystyle R_{123}=24.5\Omega

\displaystyle R_{123}=45.2\Omega

\displaystyle R_{123}=134.5\Omega

\displaystyle R_{123}=2.5\Omega

\displaystyle R_{123}=92.3\Omega

Correct answer:

\displaystyle R_{123}=24.5\Omega

Explanation:

First, calculate the equivalent resistance of \displaystyle R_2 and \displaystyle R_3. Since these two resistors are arranged in series, we just take the sum of their values.

\displaystyle R_{23}=R_{2}+R_{3}

\displaystyle R_{23}=25\Omega+38\Omega

\displaystyle R_{23}=63\Omega

With resistors 2 and 3 combined together in a single value, the following circuit is formed.

 Circuit_2

Notice that \displaystyle R_1 and \displaystyle R_{23} are arranged in parallel. To calculate the equivalent resistance of this parallel pair, we use the following equation.

\displaystyle \frac{1}{R_{123}}=\frac{1}{R_1}+\frac{1}{R_{23}}

Plug in the values, and solve for \displaystyle R_{123}.

\displaystyle \frac{1}{R_{123}}=\frac{1}{40\Omega}+\frac{1}{63\Omega}

\displaystyle R_{123}=24.5\Omega

This is just like the circuit shown below.

Circuit_3

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