Transient Circuits

Question 1

What is the voltage across a capacitor equal to

Answer 1

1/C * the integral from 0 to t of current with respect to time

Question 2

Derive the formula for charging a capacitor

Answer 2

set up basic capacitor discharge circuit with switch cell capacitor and resistor
set up equation for voltage Vs = Vr + Vc
replace Vr with I*R and Vc with 1/C integral of Idt
differentiate all with respect to time
separate variables, and integrate either side
initial condition t=0 Vc = 0
rearrange for current
I = Io *e^-t/RC

Question 3

What is the time constant

Answer 3

is a measure of how quickly a circuit can respond to change it is only dependent on RC for a capacitor circuit and R/L for an inductive circuit

Question 4

What is the voltage across the resistor in capacitor charging circuit

Answer 4

Vs*e^-t/RC

Question 5

What is the voltage across a capacitor as it is charged

Answer 5

Vs(1-e^-t/RC)

Question 6

Derive the formula for current growth in an inductor

Answer 6

See paper

Question 7

What is the formula for voltage across an inductor

Answer 7

VL=Vs*e^Rt/L

Question 8

What is the dimensions of the time constant

Answer 8

seconds

Question 9

In happens to the current growth in an inductor circuit with large time

Answer 9

The circuit reaches steady state and this is no further change in value of the current therefore the voltage across the inductor is zero therefore whole supply is dropped across the resistor

Question 10

Difference between transient and ac circuits

Answer 10

generally transient circuits will have varying current but it will remain unidirectional
ac current will flow both ways