Chapter 35, Problem 54A

What is the current in the battery of the circuit shown below? (What must you find before you can calculate the current?)

To determine

The current through the battery.

Answer to Problem 54A

The current through the battery is $0.5\text{A}$ .

Explanation of Solution

Given info:

Voltage of the battery, $V=10\text{V}$

Resistance of the parallel resistors, $R_p=30\Omega$

Resistance of the series resistors, $R_s=5\Omega$

Formula used:

The expression to calculate the equivalent resistance of the circuit is,

  $R=R_s+\frac{R_p}{2}$

The expression to calculate the current in the battery is,

  $I=\frac{V}{R}$

Calculation:

Substitute given values in the above expression.

  $\begin{array}{c}R=5\Omega +\left(\frac{30\Omega }{2}\right)\\ =5\Omega +15\Omega \\ =20\Omega \end{array}$

Substitute given values in the above expression.

  $\begin{array}{c}I=\frac{10\text{V}}{20\Omega }\\ =0.5\text{A}\end{array}$

Conclusion:

The current through the battery is $0.5\text{A}$ .