Use the definition of mutual inductance

Mutual inductance $M$ is defined from the relation $e = M\frac{dI}{dt}$ where:

• $e$ = induced emf
• $I$ = current

Write dimensions of each quantity

The dimension of emf is the same as potential difference: $[e] = [V] = [M L^2 T^{-3} A^{-1}]$

Also, $\left[\frac{dI}{dt}\right] = [A T^{-1}]$

Find the dimension of mutual inductance

From $e = M\frac{dI}{dt}$ we get $[M] = \frac{[e]}{[dI/dt]}$

Therefore, $[M] = \frac{[M L^2 T^{-3} A^{-1}]}{[A T^{-1}]}$

$[M] = [M L^2 T^{-2} A^{-2}]$

Match with the options

• A: $[M L^2 T^{-2} A^{-1}]$ ✗
• B: $[M L^2 T^{-3} A^{-1}]$ ✗
• C: $[M L^2 T^{-2} A^{-2}]$ ✓
• D: $[M L^2 T^{-3} A^{-2}]$ ✗

Conclusion

The correct dimension of mutual inductance is $[M L^2 T^{-2} A^{-2}]$ so the correct option is C.