Reactance of a capacitor is
Inversely proportional to frequency
Capacitive reactance is inversely proportional to frequency — option 3.
The formula.
\(X_{C}=\dfrac{1}{2\pi fC}\)
where f is the frequency in hertz and C the capacitance in farads. Since f appears in the denominator to the first power, doubling the frequency halves the reactance — an inverse, not an inverse-square-root, relation.
Why it behaves so. A capacitor blocks the steady flow of charge but responds to change. At a higher frequency the applied voltage reverses more often, so the plates are charged and discharged more often, and more charge moves through the circuit in each second — that is, the current is larger and the opposition smaller. At the limit :
| Frequency | Reactance | Behaviour |
|---|---|---|
| f → 0 (direct current) | Infinite | The capacitor blocks DC completely |
| Low | Large | Passes little current |
| High | Small | Passes current readily |
| f → ∞ | Zero | Behaves as a short circuit |
The contrast with an inductor. Inductive reactance is
\(X_{L}=2\pi fL\)
which rises with frequency. The two therefore oppose each other, and at the frequency where they are equal the circuit is in resonance :
\(f_{r}=\dfrac{1}{2\pi\sqrt{LC}}\)
Where this is used. The blocking of DC and passing of AC is exactly what a coupling capacitor does between amplifier stages, and a bypass capacitor uses the same property to send high-frequency signals to earth while leaving the DC bias untouched. Filters, tuning circuits in radio receivers, and the smoothing capacitor of a power supply all rest on the frequency dependence of XC.
A note on units. Reactance is measured in ohms, like resistance, but unlike a resistor it dissipates no power — the energy is stored in the electric field and returned to the circuit each cycle.
Hence, the answer is inversely proportional to frequency.
Similar Questions
An electron of mass M kg and charge e coulomb travels from rest through a potential difference of V volts. The final energy in joules would be
Which of the following is the resistance of the wire ?
Important Questions from Current Electricity
- In a parallel combination of resistors, which of the following quantities remains the same across all the resistors?
- Which of the following statements is/are true for a domestic circuit?
(i) All the appliances are connected in parallel.
(ii) The live wire in the domestic circuit has green insulation on it.
(iii) A fuse connected to the circuit allows excessive current to pass through the appliances.
(iv) The neutral wire in the domestic circuits has black insulation on it. A science teacher asks students to measure the current through a bulb using an ammeter. What precaution must the students follow?
- Which characteristic of parallel circuits makes them advantageous over series circuits for connecting multiple electrical gadgets in a house?
- In a domestic electric circuit, the main purpose of a FUSE is ________.
