Question

Two solenoids are part of the spark coil of an automobile. When the current in one solenoid falls from $\mathbf{6}\mathbf{.}\mathbf{0}\mathit{A}$to zero in 2.5ms, an emf of 30 kVis induced in the other solenoid. What is the mutual inductance M of the solenoids?

Short answer

Short Answer is Missing in the Doucument

Step-by-step solution

Given

$\epsilon =30kV=30\times {10}^{3}V$

$\frac{di}{dt}=\frac{6.0A}{2.5ms}=\frac{6.0A}{2.5\times {10}^{-3}s}$

Understanding the concept

We have the formula for the induced emf in terms of the mutual inductance in the solenoid and we can rearrange the formula to get the value for the mutual inductance.

$\epsilon =M/|di/dt|$

Calculate the mutual inductance M of the solenoids 

We have,

$$\begin{gathered} \epsilon =M/|di/dt| \\ M=\frac{\epsilon }{\left|{\displaystyle \frac{di}{dt}}\right|} \\ M=\frac{30\times {10}^3}{\left|{\displaystyle \frac{6}{2.5\times {10}^{-3}}}\right|} \\ M=12.5H\approx 13H \end{gathered}$$

Mutual inductance of the coil is 13H