Question

Question: Four 18.0 Ω resistors are connected in parallel across a 25.0 V ideal battery. What is the current through the battery?

Short answer

Answer

The value of the current is$I=5.56\text{A}$ .

Step-by-step solution

Write the given data:

1. The value of each resistor is$R=18.0\Omega$
2. The potential of the battery is$V=25.0\text{V}$

Determine the concept

Use the concept of Ohm’s law and the equivalent resistance of the parallel circuit. First, find the equivalent resistance and then, using that value in Ohm’s law formula, find the current through the battery.

Write the formula for the Ohm’s law and the equivalent resistance as:

$$\begin{gathered} V=IR \\ \frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+\frac{1}{R_4} \end{gathered}$$

Calculate the current through the battery  

First, calculate the equivalent resistance as follows:

$$\begin{gathered} \frac{1}{R_{eq}}=\frac{1}{18}+\frac{1}{18}+\frac{1}{18}+\frac{1}{18}=\frac{4}{18} \\ \frac{1}{R_{eq}}=\frac{4}{18} \\ {R}_{eq}=\frac{18}{4} \\ {R}_{eq}=4.5\Omega \end{gathered}$$

Using this value in Ohm’s law formula and solve as:

$$\begin{gathered} V=IR \\ I=\frac{V}{R} \\ I=\frac{25.0}{4.50} \\ I=5.56\text{A} \end{gathered}$$