COMEDK · Physics · 23. Alternating Current

A DC ammeter and a hot wire ammeter are connected to a circuit in series. When a direct current is passed through circuit, the DC ammeter shows \(6 \mathrm{~A}\). When \(\mathrm{AC}\) current flows through circuit, what is the average readings in \(\mathrm{DC}\) ammeter and the \(\mathrm{AC}\) ammeter, if \(\mathrm{DC}\) and AC currents flow simultaneously through the circuit?

A \(\mathrm{DC}=6 \mathrm{~A}, \mathrm{AC}=10 \mathrm{~A} \quad\)
B \(\mathrm{DC}=3 \mathrm{~A}, \mathrm{AC}=5 \mathrm{~A}\)
C \(\mathrm{DC}=5 \mathrm{~A}, \mathrm{AC}=8 \mathrm{~A} \quad\)
D \(\mathrm{DC}=2 \mathrm{~A}, \mathrm{AC}=3 \mathrm{~A}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\mathrm{DC}=6 \mathrm{~A}, \mathrm{AC}=10 \mathrm{~A} \quad\)

Step-by-step Solution

Detailed explanation

A DC ammeter measures the average value of the current passing through it. When a DC current \(I_{DC}\) and an AC current \(I_{AC}(t) = I_0 \sin(\omega t)\) flow simultaneously, the total current is \(I(t) = I_{DC} + I_0 \sin(\omega t)\). The reading of the DC ammeter is the…

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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