Скачать или смотреть A galvanometer (G) of 2Ω resistance is connected in the given circuit. The ratio of charge stored ..

A galvanometer (G) of 2Ω resistance is connected in the given circuit. The ratio of charge stored ..


Charging a capacitor involves connecting it to a voltage source, causing charge to accumulate on its plates until the voltage across the capacitor equals the source voltage. This process is governed by the relationship Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. In a circuit with a resistor (an RC circuit), charging follows an exponential curve determined by the RC time constant (τ = RC), with the charge Q(t) increasing from 0 to Q_max (CV) over time. 

The Charging Process

Connection to a voltage source: 

When a voltage source (like a battery) is connected to an uncharged capacitor through a resistor, charge begins to move from the source to the capacitor's plates. 

Charge accumulation: 

One plate accumulates a negative charge (electrons), and the other plate accumulates a positive charge. 

Exponential increase: 

The charge (Q) and voltage (Vc) across the capacitor increase exponentially over time. The rate of this increase is dictated by the RC time constant, τ = RC. 

Capacitor fully charged: 

The charging process stops when the voltage across the capacitor's plates becomes equal to the voltage of the source. At this point, the current in the circuit drops to zero, and the capacitor holds its maximum charge (Q_max = CV). 

Key Equations for Charging 

Charge on the capacitor (Q(t)): Q(t) = Q_max * (1 - e^(-t/RC))

Q_max is the maximum charge the capacitor can hold, equal to CV.

e is the base of the natural logarithm.

t is the time elapsed.

RC is the time constant, τ.

Voltage across the capacitor (Vc(t)): Vc(t) = V * (1 - e^(-t/RC))

V is the supply voltage.

The RC Time Constant (τ) 

τ = RC

τ (tau) represents the time it takes for a capacitor to charge to approximately 63.2% of its maximum value (or discharge to 36.8% of its initial value).

A smaller RC time constant means the capacitor charges and discharges more quickly.

Energy Involved

Energy supplied by the source (Ub): Ub = CV^2 

Energy stored in the capacitor (Uc): Uc = (1/2)CV^2 

Energy lost as heat: The remaining energy, (1/2)CV^2, is lost as heat in the circuit's resistance during the charging process.