How to Calculate Steady State Voltages
Steady state voltages refers to the state of an electrical circuit in normal operations. For example, voltage levels change over time from the initial "turn on" state voltage to the steady state voltage. A good way to learn how to calculate steady state voltage and understand the steady state condition is to use a simple RC circuit where you have resistor, or "R" in series with a capacitor, or "C" powered by a voltage source, or "Vsource."
Other People Are Reading
Instructions
-
-
1
Choose an R and C for the series RC circuit. R will be in units of ohms and C will be in units of microfarads. As an example, assume R is 20 ohms and C is 5 microfarads.
-
2
Determine the value Vsource. Vsource will be in units of volts. As an example, assume V is 120 volts.
-
-
3
Determine the steady state voltage using the formula: V equals Vsource multiplied by (1-e^-t/RC), where "t" is the time elapsed since Vsource was turned on. This is Vsource multiplied by 1 minus e to the negative power of t divided by RC. You will see that Vsource is the steady state voltage as you increase t from zero to the time required to reach steady state. For example:
at t = 0 seconds
RC = 20 x 0.000005 = 0.0001
t/RC = 0/ 0.0001 = 0
e^-t/RC = e^-0 = 1
V = 120 (1-1) = 120 (0) = 0 volts
at t = 5 microseconds
RC = 20 x 0.000005 = 0.0001
t/RC = 0.000005/ 0.0001 = 0.05
e^-t/RC = e^-0.05 = 0.95
V = 120 (1-0.95) = 6 volts
at t = 1 second
RC = 20 x 0.000005 = 0.0001
t/RC = 1/ 0.0001 = 10000
e^-t/RC = e^-10000 = 0 (effectively)
V = 120 (1-0) = 120 volts (steady state)
From this, you can see that V increases from 0 volts at t = 0 to reaching a steady state voltage of Vsource = 120 volts by the time t reaches 1 second. It will stay a 120 volts as t continues to increase, which is the meaning of steady state.
-
1
References
- Photo Credit Jupiterimages/Photos.com/Getty Images
