AP Physics C DC Circuits

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 3 7 4 EQ 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 1 2.0 2 3.0 3 6.0 Eq 12.0

Sample Problem #3 Resistors in Combination or a Network of Resistors V 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

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

The circuit above has been in position a for a long time 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?