1. -RC Circuits -Household Safety
AP Physics C
Mrs. Coyle

2. RC Circuits
Resistors and Capacitors in the circuit.

3. Two Situations for RC Circuits
Steady State
Variable Current
Occurs when the capacitor is fully charged
There is no current in the branch of the fully charged capacitor (it acts as an open circuit)
The current in the other braches is constant (steady state)
While the capacitor is charging or discharging

4. Charging a Capacitor in an RC Circuit
When the switch is closed, the capacitor starts to charge and the current is at maximum.
The current decreases as the capacitor continues to charge until it reaches its maximum charge (Q = CVc)
The potential difference increases until a maximum Vc.
Once the capacitor is fully charged, the current is zero. Vc

5. Steady State RC Circuit
When the capacitor is fully charged no current flows through the branch it is in.
The capacitor has its maximum voltage.
Sign convention for the capacitor voltage is the same as a battery:
Vc is (+) when we traverse
from the (–) to the (+) plate of the capacitor
(low potential to high potential)
-| |+

6. Example 1: What is the voltage and charge of the capacitor at steady state?Vc
C=2μF
Ans: 10V, 20μC

7. Charging a Capacitor in an RC Circuit
The charge on the capacitor increases exponentially with time
q =Q(1 – e-t/RC)
t is the time constant
 = RC (unit: sec)
To find current as a function of time differentiate: q =C E (1 – e-t/RC)

8. Example 2 Derive q =Q(1 – e-t/RC).
Hint: use Kirchhoff’ loop rule and substitute I=dq/dt

9. Time Constant and U In a time t=RC then q=Q(1-e-1)=0.632Q
The time constant represents the time required for the charge to increase from zero to 63.2% of Q maximum.
The energy stored in the charged capacitor is U=½ Qe = ½ Ce2

10. Discharging a Capacitor in an RC Circuit
q = Qe-t/RC
The charge decreases exponentially

11. Discharging a Capacitor in an RC Circuit
At t =  = RC, q= Q e-1 = Qmax
In one time constant, the capacitor loses 63.2% of its initial charge
Current:

12. Example 3
When the switch is closed at steady state (when the capacitor is fully charged), what is the charge of the capacitor?
Hint: Apply Kirchhoff’s Rules
Ans: 8.0 x 10-6 C

13. Household Wiring
The utility company distributes electric power to individual homes by a pair of wires (one live and one neutral-ground) with a V of 120V
The potential of the neutral wire is taken to be zero
Each house is connected in parallel with these wires
The current and voltage are alternating

14. Short Circuit
A short circuit occurs when almost zero resistance exists between two points at different potentials
This results in a very large current
In a household circuit, a circuit breaker will open the circuit in the case of an accidental short circuit
This prevents any damage

15. Effects of Various Currents
5 mA or less
can cause a sensation of shock
generally little or no damage
10 mA
muscles contract
may be unable to let go of a live wire
100 mA
if passing through the body for 1 second or less, can be fatal
paralyzes the respiratory muscles

16. Household Safety
Why should you not plug too many appliances in the same outlet?
What is the role of a circuit breaker?
Why should you not touch an electric appliance with wet hands?
What causes human injury current or voltage?
Why is grounding used?

17. More Effects In some cases, currents of 1 A can produce serious burns
Sometimes these can be fatal burns
No contact with live wires is considered safe whenever the voltage is greater than 24 V

18. Ground Wire

19. Ground-Fault Interrupters (GFI)
Special power outlets
Used in hazardous areas
Designed to protect people from electrical shock
Senses currents (of about 5 mA or greater) leaking to ground
Shuts off the current when above this level