Capacitors + RC circuits

Question 1

current (i) in terms of capacitance

Answer 1

i = C dv/dt

*capacitance (C)
*rate of change of charge (dv/dt)

Question 2

energy (w) stored in a capacitor

Answer 2

w = 1/2 C v^2

*capacitance (C)
*voltage (v)

Question 3

voltage across a capacitor (vc) in an RC circuit with a DC voltage supplied

Answer 3

vc = Vo (1 - e^-t/RC)

*supplied voltage (Vo)
*time (t)
*resistance (R)
*capacitance (C)

Question 4

voltage across a resistor (vr) in an RC circuit with a DC voltage supplied

Answer 4

vR = Vo * e^-t/RC

*supplied voltage (Vo)
*time (t)
*resistance (R)
*capacitance (C)

Question 5

energy stored across a capacitor (wc) in an RC circuit with a DC voltage supplied at a given time

Answer 5

same equation as voltage

Wc = Wo (1 - e^-2t/RC)

*energy supplied (Vo)
*time (t)
*resistance (R)
*capacitance (C)

Question 6

energy dissipated across a resistor (wr) in an RC circuit with a DC voltage supplied at a given time

Answer 6

same equation as voltage

WR = Wo * e^-2t/RC

*energy supplied (Vo)
*time (t)
*resistance (R)
*capacitance (C)

Question 7

voltage across a capacitor (vc) in a circuit with only a resistor and a charged capacitor

Answer 7

vc = Vc * e^-t/RC

*starting voltage of charged capacitor (Vc)
*time (t)
*resistance (R)
*capacitance (C)

Question 8

voltage across a resistor (vR) in a circuit with only a resistor and a charged capacitor

Answer 8

vR = - Vc * e^-t/RC
(note minus sign: direction of current)

*starting voltage of charged capacitor (Vc)
*time (t)
*resistance (R)
*capacitance (C)

Question 9

time constant (τ)

Answer 9

τ = RC

*resistance (R)
*capacitance (C)