The ratio og intantanous charge and maximum charge on the plates of capacitor at T=RC is ??
To find the ratio of instantaneous charge (Q) and maximum charge (Qmax) on the plates of a capacitor at T=RC, we first need to understand the behavior of the charge on a charging capacitor.
When a capacitor is being charged through a resistor, the charge on the plates of the capacitor gradually increases with time. The relationship between the charge (Q) on a capacitor at any given time and the maximum charge (Qmax) it can hold is given by the equation:
Q = Qmax * (1 - e^(-t/RC))
Where:
Q = instantaneous charge on the capacitor plates at time t
Qmax = maximum charge the capacitor can hold
t = time
R = resistance
C = capacitance
At T=RC, we need to substitute the time (t) with T=RC in the equation. Let's do that:
Q = Qmax * (1 - e^(-T/RC))
Now, since T=RC, we can further simplify the equation:
Q = Qmax * (1 - e^(-1))
As e^(-1) is approximately 0.368 (a constant value), we can substitute it into the equation:
Q = Qmax * (1 - 0.368)
Hence, the ratio of instantaneous charge (Q) and maximum charge (Qmax) on the plates of the capacitor at T=RC is approximately 0.632 (calculated as 1 - 0.368).