Concept:

A choke is an inductor designed to limit AC current. For a purely inductive circuit, the opposition to the alternating current is called inductive reactance.

Formula:

The inductive reactance is defined as:

$$X_L = \omega L$$

and the current amplitude (peak current) is:

$$I_0 = \frac{E_0}{X_L}$$

Solution:

Compare the given voltage equation \( E = 100 \sin(100 \pi t) \) to the standard equation \( E = E_0 \sin(\omega t) \):

• Peak EMF, \( E_0 = 100\text{ V} \)
• Angular frequency, \( \omega = 100 \pi\text{ rad/s} \)
• Peak current, \( I_0 = 1\text{ A} \)

Substitute these values to solve for inductance \( L \):

$$I_0 = \frac{E_0}{\omega L} \implies 1 = \frac{100}{100 \pi \times L}$$

$$L = \frac{100}{100 \pi} = \frac{1}{\pi}\text{ H}$$

Why other options are incorrect:

• Other options like \( 200\text{ H} \), \( 2\pi\text{ H} \), or \( 2/\pi\text{ H} \) are incorrect due to standard errors in algebraic rearrangement, such as multiplying by \( 2 \) instead of dividing or incorrect cancellation of \( 100 \).