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DC CIRCUITSAP Physics C
Resistors in Series
What is constant? What ‘adds up’? How do you
determine the
equivalent resistance?
Sample Problem #1 The current flowing in a
circuit containing four resistors connected in series is I = 1.0 A. The potential drops across the first, second and third resistors are, respectively: V = 5 V, V = 8 V and V = 7 V. The equivalent resistance of the circuit is R = 30. Find the total voltage supplied by the battery, and also current, voltage drop, and resistance of each resistor in the circuit.
V I R P
1 5 1.0
2 8 1.0
3 7 1.0
4 1.0
EQ 1.0 30
Resistors in Parallel
What is constant? What ‘adds up’? How do you
determine the
equivalent resistance?
Sample Problem #2 Complete the VIRP
Table for the circuit shown.
V I R P
1 2.0
2 3.0
3 6.0
Eq 12.0
Sample Problem #3 Resistors in
Combination or a Network of Resistors
V I R P
1 10.0
2 4.0
3 3.0
4 8.0
5 1.0
Eq 13.4
Sample Problem #4
Determine the equivalent resistance:
Kirchhoff’s Rules
Current (Point) Rule: The total current into a junction is equal to the current out of a junction or the total current is zero.
Kirchhoff’s Rules
Voltage (Loop) Rule: The total voltage gains of the sources is equal to the total voltage drops of the loads or the total gains and drops is
zero.
Problem-Solving Strategy: Determine and label the direction of the
current in the given circuit. Apply the point rule once and then the
loop rule as many times as needed to get the same number of equations as unknowns in the circuit. Note: Follow the sign convention given on the next slide when apply the loop rule.
Sign Convention for the Loop Rule:
The loop is going from left to right.
Sample Problem #5
Find the currents:
Sample Problem #6
Find the currents:
Ammeter Design
Voltmeter Design
Sample Problem #7
The resistance of a galvanometer coil is 20 Ω and the full-scale current is 50 μA.What does the resistance of the shunt
need to be to design an ammeter that would measure up to 5.0 A?
What does the resistance of the series resistor need to be to design a voltmeter that would measure up to 100 V?
RC Circuits
Initially, the capacitor is uncharged. What is the current in the circuit when
the switch is closed; that is, at t = 0? How does the current change over time? What is the charge stored on the
capacitor at t = 0? How does the charge change
over time?
Charging a RC Circuit
Apply Kirchhoff’s Loop Rule:
Recall the definition for
current
Time Constant-Characteristic Property of a RC Circuit
Transient Values when charging a RC Circuit
At t = 0 Some t later As t ∞
Capacitor
Current
Voltage
Resistor
Current
Voltage
Discharging a RC Circuit
The capacitor has been fully charged. The source of emf has been removed. What is the current in the circuit when the switch is closed; that is, at t = 0?
What happens to the current over time? What is the charged stored on the
capacitor at t = 0? What happens to the charge over time?
Discharging a RC Circuit:
When the capacitor is fully charged, the switch is moved from a to b.
Apply Kirchhoff’s loop rule,
Voltage-Time Graphs
Sketch the Voltage-Time Graphs for discharging a RC Circuit
Transient Values when discharging a RC Circuit
At t = 0 Some t later As t ∞
Capacitor
Current
Voltage
Resistor
Current
Voltage
The circuit above has been in position a for a long time. At time t = 0 the switch is thrown to position b. DATA: Vb = 12 V, C = 10 μF, R = 20 Ω What is the curnent through the resistor just BEFORE the
switch is thrown? What is the current through the resistor just AFTER the
switch is thrown? What is the charge across the capacitor just BEFORE the
switch is thrown? What is the charge on the capacitor just AFTER the switch is
thrown? What is the charge on the capacitor at at time t = 0.3 msec
after the switch is thrown?
Considering the same circuit, only with the switch thrown from b to a at time t = 0 after having been in position b for a long time. DATA: Vb = 12 V, C = 10 μF, R = 20Ω What is the curnent through the resistor just BEFORE the switch is
thrown? What is the current through the resistor just AFTER the switch is
thrown? What is the charge across the capacitor just BEFORE the switch is
thrown? What is the charge on the capacitor just AFTER the switch is thrown? What is the charge on the capacitor at at time t = 0.3 msec after the
switch is thrown?