“There is a limit to the amount of charge that can be stored on a given capacitor.” Explain.
Solution and Explanation
Capacitor Charge Capacity
A capacitor's charge storage capacity is limited by the dielectric strength of the insulating material positioned between its conductive plates.
When the voltage applied across the capacitor reaches a critical threshold, the dielectric material degrades, initiating an electrical discharge. This degradation phenomenon dictates the maximum charge the capacitor can retain.
Charge, Capacitance, and Voltage Correlation:
The interrelation between stored charge \( Q \), capacitance \( C \), and applied voltage \( V \) is defined by the equation:
\[ Q = C \cdot V \]
Consequently, for a specific capacitor, its maximum storable charge is dictated by its capacitance value and the highest voltage it can tolerate before dielectric failure.
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A circuit consisting of a capacitor C, a resistor of resistance R and an ideal battery of emf V, as shown in figure is known as RC series circuit.
As soon as the circuit is completed by closing key S₁ (keeping S₂ open) charges begin to flow between the capacitor plates and the battery terminals. The charge on the capacitor increases and consequently the potential difference Vc (= q/C) across the capacitor also increases with time. When this potential difference equals the potential difference across the battery, the capacitor is fully charged (Q = VC). During this process of charging, the charge q on the capacitor changes with time t as
\(q = Q[1 - e^{-t/RC}]\)
The charging current can be obtained by differentiating it and using
\(\frac{d}{dx} (e^{mx}) = me^{mx}\)
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