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In an AC circuit of frequency f containing resistance R, capacitance C and inductance L, which of the following combinations has the same dimensions as R (resistance)?

1. f*C
2. f*L
3. C/f
4. L/f

Correct answer: f*L

Solution

Reactance has the dimensions of resistance (ohms). Inductive reactance X_L = 2*pi*f*L, so f*L has the dimensions of R. Capacitive reactance is 1/(2*pi*f*C), so 1/(fC) has resistance dimensions, but f*C and C/f do not. Hence f*L matches R.

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