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

RC Circuits Resistors and Capacitors in the circuit.

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

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

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) -| |+

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

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)

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

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

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

Discharging a Capacitor in an RC Circuit At t =  = RC, q= Q e-1 = 0.368 Qmax In one time constant, the capacitor loses 63.2% of its initial charge Current:

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

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

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

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

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?

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

Ground Wire

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