Capacitors (Unit 4)

Question 1

Capacitance Definition

Answer 1

Charge stored per unit potential difference

Question 2

Capacitance graphs (Q against V; V against Q)

Answer 2

Charge, Q, against Potential Difference, V
gradient is capacitance : C=Q/V
area under is energy stored by capacitor
Y = Q, X = V, Straight line proportional through the origin
Potential difference, V, against Charge, Q
gradient is 1/capacitance : 1/C = V/Q
area under is energy stored by capacitor
Y = V, X = Q, Straight line proportional through the origin

Question 3

Derivation of E=½QV

Answer 3

W = V Q explained (1)
energy stored = total work done in charging = charge x average voltage (1)
energy stored = work done (= ½QV) (1)

Question 4

Time constant definition

Answer 4

Time taken for the voltage (or charge or current) to fall to 1/e of its initial value.

Question 5

Finding time constant from a graph of Potential Difference (V) against time (t)

Answer 5

1. Calculate 1/e of initial voltage, V0
2. Locate value on graph.
3. Time taken is time constant.

Question 6

Finding time constant from a graph of ln (V) against time

Answer 6

4. ln(V) - ln(V0) =-t/RC
   5.ln(V) =-(1/RC)t + ln(V0)
5. is in form y=mx+c. Gradient is -1/RC and intercept is ln(V0)
   Time constant (RC) = - (t/gradient)

Question 7

Graphical representations of energy stored against voltage

Answer 7

Energy = ½CV2

Energy proportional to V2

Question 8

Graphical representations of charging a capacitor against time

Answer 8

V against t
I against t
Q against t

Question 9

Graphical representations of discharging a capacitor against time

Answer 9

V against t
I against t
Q against t