Presentation on theme: "-RC Circuits -Household Safety"— Presentation transcript:
1 -RC Circuits -Household Safety AP Physics CMrs. Coyle
2 RC CircuitsResistors and Capacitors in the circuit.
3 Two Situations for RC Circuits Steady StateVariable CurrentOccurs when the capacitor is fully chargedThere 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 traversefrom 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? VcC=2μFAns: 10V, 20μC
7 Charging a Capacitor in an RC Circuit The charge on the capacitor increases exponentially with timeq =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/RCThe charge decreases exponentially
11 Discharging a Capacitor in an RC Circuit At t = = RC, q= Q e-1 = QmaxIn one time constant, the capacitor loses 63.2% of its initial chargeCurrent:
12 Example 3When the switch is closed at steady state (when the capacitor is fully charged), what is the charge of the capacitor?Hint: Apply Kirchhoff’s RulesAns: 8.0 x 10-6 C
13 Household WiringThe utility company distributes electric power to individual homes by a pair of wires (one live and one neutral-ground) with a V of 120VThe potential of the neutral wire is taken to be zeroEach house is connected in parallel with these wiresThe current and voltage are alternating
14 Short CircuitA short circuit occurs when almost zero resistance exists between two points at different potentialsThis results in a very large currentIn a household circuit, a circuit breaker will open the circuit in the case of an accidental short circuitThis prevents any damage
15 Effects of Various Currents 5 mA or lesscan cause a sensation of shockgenerally little or no damage10 mAmuscles contractmay be unable to let go of a live wire100 mAif passing through the body for 1 second or less, can be fatalparalyzes the respiratory muscles
16 Household SafetyWhy 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 burnsNo contact with live wires is considered safe whenever the voltage is greater than 24 V
19 Ground-Fault Interrupters (GFI) Special power outletsUsed in hazardous areasDesigned to protect people from electrical shockSenses currents (of about 5 mA or greater) leaking to groundShuts off the current when above this level
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