# Transients

#### Steve1992

Joined Apr 7, 2006
100
I saw this question on transients:

0.1uF cap. in series with 10k resistor.
Combination connected to 100V dc.

Q. 'The initial rate of rise of the pd across the capacitor?'
A. '100 kV/s'

I assumed the initial voltage across cap. would be zero?

#### Papabravo

Joined Feb 24, 2006
16,984
It is. What do you think "rate of rise" refers to?

#### Dave

Joined Nov 17, 2003
6,970
Papabravo is correct. The initial steady-state voltage across the capacitor is 0V, however the voltage across the capacitor will increase at a rate of 100kV per second (no longer in steady-state conditions) so every second the voltage across the capacitor would in theory increase by 100kV. It would in fact reach steady state conditions of 100V across the capacitor very quickly; 1ms if I have done my maths right.

Dave

#### Papabravo

Joined Feb 24, 2006
16,984
Also note that, as in all cases where the solution to a differential equation is an exponential function, the rate of rise decreases monotonically as the voltage approaches it's steady state value asymptotically.

#### Ron H

Joined Apr 14, 2005
7,014
Papabravo is correct. The initial steady-state voltage across the capacitor is 0V, however the voltage across the capacitor will increase at a rate of 100kV per second (no longer in steady-state conditions) so every second the voltage across the capacitor would in theory increase by 100kV. It would in fact reach steady state conditions of 100V across the capacitor very quickly; 1ms if I have done my maths right.

Dave
The time constant is 1mS. The voltage on the cap will theoretically never reach 100V, because, as Papabravo says, it will approach that value asymptotically. In five time constants, it will charge to 99.326V, which is generally accepted as fully charged.

#### Dave

Joined Nov 17, 2003
6,970
The time constant is 1mS. The voltage on the cap will theoretically never reach 100V, because, as Papabravo says, it will approach that value asymptotically. In five time constants, it will charge to 99.326V, which is generally accepted as fully charged.
You are correct about the RC time constant and the fact that the voltage across the capacitor approaches the 100V source voltage asymptotically. The general point I was making was that the rate of rise of the voltage across the capacitor is the intermediate transition from the initial steady-state 0V to a steady-state ~100V. This is a simplification of the reality but demonstrates the point raised in the OP.

Thanks for the clarification.

Dave