Consider the following circuit shown in Fig. Q38 and read the following statements.Statement 1:The current through the capacitor can be obtained by using only source transformation without the use of superposition theorem.Statement 2:The current through the capacitor can be obtained by using superposition theorem. Fig. Q38Choose the correct option from the following:
Original figure referenced in question 38.
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Answer & Explanation
Correct AnswerC. Statement 2 is correct, but statement 1 is incorrect.
Quick Explanation
The network is linear, so superposition can be used by analyzing the response to each sinusoidal source at its own frequency and then adding the time-domain currents. Because the two sources operate at different frequencies and the reactive impedances are frequency-dependent, a single phasor-domain source transformation cannot combine the complete problem without separate frequency analysis. Thus statement 1 is false and statement 2 is true.
Formula / Key Relation
iC(t)=iC,ω=2(t)+iC,ω=10(t)
Detailed Explanation
Correct Answer
C — Statement 2 is correct, but statement 1 is incorrect.
Statement-wise Analysis
Statement 1: False
Statement 2: True
Concept and Reasoning
The network is linear, so superposition can be used by analyzing the response to each sinusoidal source at its own frequency and then adding the time-domain currents. Because the two sources operate at different frequencies and the reactive impedances are frequency-dependent, a single phasor-domain source transformation cannot combine the complete problem without separate frequency analysis. Thus statement 1 is false and statement 2 is true.
Calculation / Key Relation
iC(t)=iC,ω=2(t)+iC,ω=10(t)
Exam Takeaway
Different frequencies → solve separately, then superpose in time.
Common Mistake
Do not add phasors belonging to different frequencies.
Quick Trick
Different frequencies → solve separately, then superpose in time.
Common Mistake
Do not add phasors belonging to different frequencies.
Exam Tip
Different frequencies → solve separately, then superpose in time.
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