Question

Explain the term capacitive reactance. State its unit and dimensions.

Answer 1

1. The peak value of alternating current through a capacitor is given by,
   i₀ = `"e"_0/((1"/" omega"C"))` ….(1) 
2. For a capacitive a.c. circuit, According to Ohm’s law,
   i = `"V"/"R"` ….(2)
   where R = resistance of the circuit.
3. Comparing equations (1) and (2), we conclude that `(1/(omega"C"))` plays a similar role in capacitive AC circuit as resistance in a purely resistive circuit.
4. Hence, the effective resistance (X_C) offered by the capacitor C is given as, 
   X_C = `1/(omega"C") = 1/(2pi"fC")` ......`(∵ omega = (2pi)/"T" = 2pi"f")`
   Where f = frequency of AC supply
5. The function of capacitive reactance in a purely capacitive circuit is to limit the amplitude of the current similar to the resistance in a purely resistive circuit.
6. X_C varies inversely as the frequency of AC and also as the capacitance of the condenser.
7. In a DC circuit, f = 0
   ∴ X_C = ∞
   Thus, the capacitor blocks DC and acts as an open circuit while it passes AC of high frequency.
8. The dimensions of capacitive reactance are [ML²T^-3I ^-2] and its SI unit is the ohm (Ω).