Chapter 20, Problem 56P

To determine

The current that will give full-scale deflection.

Answer to Problem 56P

  $27 \text{μA}$ current will give full-scale deflection if it originally required $36 \text{μA}$

Explanation of Solution

Given:

The spring constant decreases by $25\%$ . The original amount of current was $36 \text{μA}$

Formula used:

The deflection is proportional to the ratio of current and the spring constant.

  $\varphi \propto \frac{I}{k}$

Calculation:

Since deflection is proportional to the ratio of current and spring constant. If the spring constant decreases so will be the current to produce the same amount of deflection. Thus, if the current decreases by $25\%$ then the revised current detected will be $75\%$ of the original one. On comparing, the old data and revised values,

  $\begin{array}{c}{I}_{final}=0.75I_{initial}\\ I_{final}=0.75\times 36 \text{μA}\\ =27 \text{μA}\end{array}$

Conclusion:

Therefore, $27 \text{μA}$ current will give full-scale deflection if it originally required $36 \text{μA}$