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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)?
- f*C
- f*L
- C/f
- 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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