Referring to the given circuit, match column-I with column-II:

Column-IColumn-II(i) For ω = 8000 r…

Question

Referring to the given circuit, match column-I with column-II:

Column-IColumn-II(i) For ω = 8000 rad/s[A] Peak current in the circuit is less than 0.1 A(ii) For ω = 10000 rad/s[B] Voltage across the combination and the current are in same phase(iii) For ω = 10500 rad/s[C] Voltage across the combination leads the current(iv) For ω = 10000 rad/s, if R = 50 Ω instead of 100 Ω[D] Current through the circuit leads the voltage across it

CGP EDU Academic Team · Accepted Answer

The correct answer is B. Step 1: Analyze the circuit provided, which consists of a resistor (R) and an inductor (L) in series with an AC voltage source.  Step 2: For different frequencies (ω), we need to determine the behavior of the current and voltage in relation to each other. Step 3: For ω = 8000 rad/s, the peak current is expected to be low due to impedance, thus matching with option [A]. Step 4: For ω = 10000 rad/s, we observe that the circuit is at resonance (assuming this is the resonant frequency). At this frequency, the voltage across the components and the current are in phase. This matches with option [B]. Step 5: For ω = 10500 rad/s, which exceeds the resonant frequency, the voltage will lead the current, matching option [C]. Step 6: When R is decreased to 50 Ω at the same frequency of 10000 rad/s, more current will flow, leading the voltage, consistent with option [D].  Thus, the correct match for item (ii) is option [B].

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Column-I	Column-II
(i) For ω = 8000 rad/s	[A] Peak current in the circuit is less than 0.1 A
(ii) For ω = 10000 rad/s	[B] Voltage across the combination and the current are in same phase
(iii) For ω = 10500 rad/s	[C] Voltage across the combination leads the current
(iv) For ω = 10000 rad/s, if R = 50 Ω instead of 100 Ω	[D] Current through the circuit leads the voltage across it

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