Example from Physics, 19.3 Parallel Circuits

Find the Current through Parallel Resistors

The three circuits below are equivalent. If the voltage rating of the battery is $V_{battery} = 3 V$ , what is the equivalent resistance of the circuit and what current runs through the circuit?

Three equivalent circuit diagrams are shown, each with three resistors connected in parallel.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
The three resistors are connected in parallel and the voltage drop across them is V_battery. Thus, we can apply the equation for the equivalent resistance of resistors in parallel, which takes the form

$R_{equiv} = \frac{1}{1 / R_{1} + 1 / R_{2} + 1 / R_{3}} .$
19.29

The circuit with the equivalent resistance is shown below. Once we know the equivalent resistance, we can use Ohm’s law to find the current in the circuit.
Solution
Inserting the given values for the resistance into the equation for equivalent resistance gives

$\begin{matrix} R_{equiv} & = & \frac{1}{1 / R_{1} + 1 / R_{2} + 1 / R_{3}} \\ = & \frac{1}{1 / 10 Ω + 1 / 25 Ω + 1 / 15 Ω} \\ = & 4.84 Ω. \end{matrix}$
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The current through the circuit is thus

$\begin{matrix} V & = & I R \\ I & = & \frac{V}{R} \\ = & \frac{3 V}{4.84 Ω} \\ = & 0.62 A. \end{matrix}$
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0 of 2 steps open

How did it go?

Strategy

Solution

Strategy

Solution