Join thousands of students who trust us to help them ace their exams!Watch the first video
Multiple Choice
The peak current to and from an inductor is when the emf source has a peak voltage and frequency . What is the peak current to and from the inductor if the frequency and peak voltage are doubled to and . respectively?
A
B
C
D
E
Verified step by step guidance
1
Understand that the peak current through an inductor in an AC circuit is determined by the inductive reactance, which is given by the formula: \( X_L = 2\pi f L \), where \( f \) is the frequency and \( L \) is the inductance.
The peak current \( I_L \) is related to the peak voltage \( V \) and the inductive reactance \( X_L \) by the formula: \( I_L = \frac{V}{X_L} \).
When the frequency \( f \) is doubled to \( 2f \), the inductive reactance becomes \( X'_L = 2\pi (2f) L = 4\pi f L = 2X_L \).
Similarly, when the peak voltage \( V \) is doubled to \( 2V \), the new peak current \( I'_L \) is given by: \( I'_L = \frac{2V}{2X_L} = \frac{V}{X_L} = I_L \).
Thus, the peak current remains the same, \( I'_L = I_L \), even when both the frequency and peak voltage are doubled.