Chapter 25, Problem 98A

To determine

To calculate:

The potential difference over a $22$ O current with $5.0$ W resistor which is operating at half its rating.

Answer to Problem 98A

The potential difference over a $22$ O current with $5.0$ W resistor which is operating at half of its rating is $7.4$ V.

Explanation of Solution

Given:

Resistance: $22$ O

Power: $5.0$ W

Formula Used:

Formula for power is given by,

  $P=\frac{V^2}{R}$

Where,

  $P$ : Power

  $R$ : Resistance

  $V$ : Voltage

Calculation:

Formula to calculate the power is used to find the potential difference over a resistor.

  $P=\frac{V^2}{R}$

Rearrange the formula of Power to calculate the potential difference.

  $V=\sqrt{PR}$

Taking the square root for the power and resistance and

Substitute all the given values in the above formula,

  $V=\sqrt{\left(5.0\right)\times \left(22\right)}$

As the resistor is operating at half of its rating,

  $V=\sqrt{\frac{\left(5.0\right)}{2}\times \left(22\right)}$$=$$\sqrt{\left(5.0\right)\times \left(11\right)}$

  $=$$\sqrt{\left(55\right)}$

  $V=7.4$ V

Conclusion:

Hence, the potential difference over a $22$ O current and $5.0$ W resistor which is operating at half of its rating is $7.4$ V.