A capacitor of 5 microfarads is connected to an A.C source of frequency 50Hz. The capacitive reactance is:

Physics

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Answer

636.62 Ω636.62 \text{ } \Omega

Step-by-step solution

3 steps
  1. Convert the capacitance from microfarads to farads.

    C=5 μF=5×10−6 FC = 5 \text{ } \mu\text{F} = 5 \times 10^{-6} \text{ F}
  2. Use the formula for capacitive reactance.

    XC=12πfCX_C = \frac{1}{2 \pi f C}
  3. Substitute the given values into the formula.

    XC=12π(50 Hz)(5×10−6 F)X_C = \frac{1}{2 \pi (50 \text{ Hz}) (5 \times 10^{-6} \text{ F})} XC=12π(250×10−6)X_C = \frac{1}{2 \pi (250 \times 10^{-6})} XC=10.001570796X_C = \frac{1}{0.001570796} XC≈636.62 ΩX_C \approx 636.62 \text{ } \Omega

    The capacitive reactance is approximately 636.62 Ω\Omega.

    636.62 Ω636.62 \text{ } \Omega
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