Question

In ac circuit containing an ac source of frequency f, the capacitance is proportional to

Hint:

Read carefully!
- Resistance ($R$), Inductance ($L$), Capacitance ($C$) are physical component properties, generally independent of frequency.
- Inductive reactance ($X_L \propto f$) and Capacitive reactance ($X_C \propto 1/f$) are circuit properties that strongly depend on frequency.

Answer 1

Step 1: Understanding the Concept:
It is critical to distinguish between 'capacitance' ($C$) and 'capacitive reactance' ($X_C$).
- Capacitance is an intrinsic physical property of a capacitor, determined by its geometry (plate area, separation) and the dielectric material between the plates ($C = \epsilon A / d$). It describes its ability to store charge.
- Capacitive Reactance is the opposition a capacitor offers to alternating current in an AC circuit. This opposition depends on how fast the voltage is changing.

Step 2: Key Formula or Approach:
Capacitive reactance is calculated as:
\[ X_C = \frac{1}{2\pi f C} \]
Where $f$ is the frequency of the AC source.

Step 3: Detailed Explanation:
The literal text of the question asks what the capacitance is proportional to regarding frequency.
Based on the physical definition, a 10 $\mu$F capacitor has a capacitance of 10 $\mu$F whether it is connected to a 50 Hz source, a 1 MHz source, or a DC battery.
Therefore, capacitance is a constant with respect to frequency. It is proportional to $f^0$.
However, questions worded like this often contain a typo and intend to test the knowledge of reactance. If the question meant to ask about capacitive reactance, then from the formula $X_C = \frac{1}{2\pi f C}$, we can see that $X_C$ is inversely proportional to frequency:
\[ X_C \propto \frac{1}{f} \]

Step 4: Final Answer:
Literally, capacitance is independent of frequency. It is highly likely the question meant capacitive reactance, which is proportional to $1/f$.