RC Circuits Charging CapacitorThe capacitor is neutralNo current flows through the circuit
RC Circuits Charging CapacitorThe switch is closedMaximum current flows
RC Circuits Charging Capacitor +q -q +q +q goes to lower part of capacitor +q is repelled from upper part of capacitor leaving a -q chargeAs the lower plate increases in + charge, current decreases due torepulsion
RC Circuits Charging Capacitor +q -Q +Q +q +qThis process repeats until the capacitor gains and emf equal toand plates with charges +Q and -QFinally, the current is zero due to maximum charge repulsion
SeatworkFind(a) the time constant of the circuit and(b) the maximum charge on the capacitor afterthe switch is closed.(c) If the switch is closed at t = 0, ﬁnd thecurrent in the resistor 10.0 s later.
RL Circuits Current GrowthOn a 1 whole sheet of paper(a) What is the initial battery current immediately after switch S is closed?(b) What is the battery current a long time after switch S is closed?
RL Circuits Current GrowthThe switch is openNo current flows through the circuit
RL Circuits Current GrowthThe switch is closedCurrent flows through the circuit but is delayed by inductor
RL Circuits Current GrowthWe can write Kirchhoff’s loop rule
RL CircuitsCurrent Growth at t = 0 current starts at zero increases as time passes
RL Circuits Current DecaySwitch S1 is closed, S2 is openCurrent flows through RL circuit through S1.After sometime, the current becomes maximum
RL Circuits Current Decay S1Switch S1 is opened, S2 is closedCurrent flows through RL circuit through S2.
RL Circuits Current Decay S1The current decreases but the diminishing rate is reduced by thepresence of the inductor.
RL Circuits Current Decay S1We can write Kirchhoff’s Loop Rule
RL CircuitsCurrent Decay Current decreases as time passes but not instantaneously zero! This is due to the inductor. “Resists Change”
LC CircuitsOscillating chargeOscillating current frequency of oscillation
LC CircuitsExampleThe capacitor is initially charged whenswitch S1 is open and S2 is closed. SwitchS1 is then thrown closed at the sameinstant that S2 is opened, so that thecapacitor is connected directly across theinductor. (a) Find the frequency ofoscillation of the circuit.
Seatwork1. An LC circuit consists of a 20.0-mH inductor and a 0.500-µF 1a: 10k rad/s 1b: 20 V capacitor. If the maximum instantaneous current is 0.100 A 2.608. pF (a) What is the frequency of current oscillation? 3.a 134.8 Hz 3.b. 119 uC (b) What is the greatest potential difference across the 3.c. 0.101 A capacitor? 4.200*2^(0.5) cos(2 pi 100 Hz t) Volts 5.a 193 ohms 5.b 145 ohms2. A ﬁxed inductance L = 1.05 µH is used in series with a variable capacitor in the tuning section of a radio. What capacitance tunes the circuit to the signal from a station broadcasting at 6.30 MHz?3. An LC circuit contains an 82.0-mH inductor and a 17.0-µF capacitor that initially carries a 180-µC charge. The switch is thrown closed at t = 0. (a) Find the frequency (in hertz) of the resulting oscillations. (b) At t = 1.00 ms, ﬁnd the charge on the capacitor and (c) the current in the circuit.4. The rms output voltage of an ac generator is 200 V, and the operating frequency is 100 Hz. Write the equation giving the output voltage as a function of time.5. (a) What is the resistance of a lightbulb that uses an average power of 75.0 W when connected to a 60.0-Hz power source having a maximum voltage of 170 V? (b) What is the resistance of a 100-W bulb?