AP EAMCET · PHYSICS · Alternating Current

In the \(A C\) circuit shown,
\[
\begin{aligned}
& E=E_0 \sin (\omega t+\phi) \text { and } \\
& i=i_0 \sin \left(\omega t+\phi+\frac{\pi}{4}\right) .
\end{aligned}
\]
Then, the box contains

A Only C
B L and R in series
C C and R in series or L, C and R in series
D Only R

Verified Solution

Answer & Solution

Correct Answer

(C) C and R in series or L, C and R in series

Step-by-step Solution

Detailed explanation

As current leads by \(\frac{\pi}{4}\), so circuit must be more capacitive them inductive. Hence, it is either a \(C-R\) combination or \(L-C-R\) combination.

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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In the \(A C\) circuit shown,\[\begin{aligned}& E=E_0 \sin (\omega t+\phi) \text { and } \\& i=i_0 \sin \left(\omega t+\phi+\frac{\pi}{4}\right) .\end{aligned}\]Then, the box contains

Step-by-step Solution

In the \(A C\) circuit shown,
\[
\begin{aligned}
& E=E_0 \sin (\omega t+\phi) \text { and } \\
& i=i_0 \sin \left(\omega t+\phi+\frac{\pi}{4}\right) .
\end{aligned}
\]
Then, the box contains