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 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. \[ \boxed{\text{Capacitance}} \]