Question

The function \( \frac{dq}{dv} \) is called incremental then it is

• A. Resistance
• B. Capacitance
• C. Inductance
• D. Frequency

Hint:

For a linear capacitor, \(C = q/v\). The derivative \(dq/dv = C\).
For non-linear capacitors, the incremental capacitance \(C(v) = dq/dv\) describes how much additional charge is stored for an incremental change in voltage.

Answer 1

The Correct Option is B

The fundamental relationship for a capacitor is \( q = Cv \), where \( q \) is the charge, \( C \) is the capacitance, and \( v \) is the voltage.

If the capacitance is constant, differentiating with respect to voltage gives: \[ \frac{dq}{dv} = \frac{d}{dv}(Cv) = C \] 

If the capacitance itself is a function of voltage (as in some non-linear capacitors like varactors), then the incremental capacitance (or differential capacitance) is defined as \( C_{inc} = \frac{dq}{dv} \). This quantity represents the rate of change of charge with respect to voltage at a particular operating point.

Considering the other options: 
Resistance (R): Related by Ohm's law \( v = iR \). Also, \( i = \frac{dq}{dt} \). The derivative \( \frac{dq}{dv} \) is not directly resistance. 
Inductance (L): Related by \( v = L \frac{di}{dt} \). This involves the rate of change of current. 
Frequency (f): A characteristic of periodic signals, not directly defined by \( \frac{dq}{dv} \).

Thus, \( \frac{dq}{dv} \) represents capacitance, or more specifically, incremental capacitance if \( C \) is not constant.

Conclusion: \[ \boxed{\text{Capacitance}} \]