Chapter 26 DC Circuit
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Transcript of Chapter 26 DC Circuit
Bareza Physics 72 2nd sem AY 15-16 1
Direct-Current DC direction of the current does not change with time
Alternating-Current AC current oscillates back and forth
Direct-Current Circuits
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26-1 Resistors in Series and Parallel
26-2 Kirchoff’s Rules
26-4 RC Circuits
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OBJECTIVES:
҉ Given a network of resistors connected in series and/or parallel, evaluate the equivalent resistance, current and voltage
҉ Evaluate the voltage drop and current passing through each element circuit
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Ch26-1
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Resistor
Resistance R (unit:
Ω) – impedes current
flow and acts to
lower voltage levels
within circuits.
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Four ways to connect 3 resistors
with resistances R1, R2, R3
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Equivalent resistance
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Resistors in Series
Current I must be the same in all resistors.
Their potential differences add.
Recall: Equivalent resistance of 3 resistors
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Resistors in Series
Equivalent resistance of n resistors
In general, for n number of resistors,
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Resistors in Parallel
Potential difference is the same for all resistors.
Their currents add.
Recall:
Equivalent resistance of 3 resistors
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Resistors in Parallel
Equivalent resistance of n resistors
In general, for n number of resistors,
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Ch26-1
Example:Compute the equivalent resistance of the network
shown, and find the current in each resistor. The
battery has negligible internal resistance.
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Ch26-1
Seatwork:In the circuit shown, each resistor represents a light bulb.
Let R1= R2 = R3 = R4 = 1 Ω and ε = 9.00 V.
a) Find the equivalent resistance of the network.
b) Find the current (I1, I2, I3, I4) in each bulb.
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Another exampleConsider the circuit shown. The current through the
6.00-Ω resistor is 4.00 A, in the direction shown. What
are the currents through the 25.0-Ω and 20.0-Ω
resistors?
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26-1 Resistors in Series and Parallel
26-2 Kirchoff’s Rules
26-4 RC Circuits
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OBJECTIVE:
҉ Given a circuit diagram, calculate the current through and voltage across a circuit element using Kirchoff’s loop and junction rules
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Ch26-2
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Ch26-2
Many practical resistor networks cannot be reduced to simple
series-parallel combinations.
Kirchhoff’s
Rules
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Examples:
A junction in a circuit is a point where three or more conductors meet.
• (node or branch point)
A loop is any conducting path.
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1. Kirchhoff’s Junction RuleThe algebraic sum of the currents into any junction is zero.
The junction rule is based on conservation of electric charge.
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2. Kirchhoff’s Loop RuleThe algebraic sum of the potential differences in any loop,
(including those associated with emfs and those of resistive elements),
must equal to zero.
The loop rule is a statement that the electrostatic force is
conservative.
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2. Kirchhoff’s Loop Rule
Sign Conventions:
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Example:Consider the circuit fragment shown in the figure. What
is the current IX flowing out of node B?
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Example:Using the circuit diagram below use junction rule to
express the relationship of the assumed current
direction.
I1
I2
I3
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Example:
I. -I1 R1 - I2 R2 - V1 = 0
II. I1 R1 + I3 R3 + V2 = 0
III. -I2 R2 - I4 R4 - V2 = 0
Consider the circuit shown with the
assumed direction of each branch
current shown by the labeled arrows.
Assuming each inner loop is
travelled counterclockwise, which
of the following equations follows
Kirchhoff's voltage law?
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Ch26-2
Example:In the circuit shown, find
(a) the current in the 3.00-Ω resistor;
(b) the unknown emfs ε1 and ε2;
(c) the resistance R.
Note that three currents are given.
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Ch26-2
Example:What is the internal resistance r in the 12-V battery?
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In the circuit shown, find
(a)the current in resistor R;
(b)the resistance R;
(c)the unknown emf ε.
(d)If the circuit is broken at point x,
what is the current in resistor R?
Seatwork:
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26-1 Resistors in Series and Parallel
26-2 Kirchoff’s Rules
26-4 RC Circuits
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OBJECTIVE:
҉ Describe the behaviour of current, potential, and charge as a capacitor is charging or discharging in terms of the initial and steady-state conditions
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Ch26-4
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R-C CircuitA circuit that has a resistor and a capacitor in series
1. Current changes with time
2. Voltage changes with time
3. Power changes with time
Charging/Discharging a Capacitor
heart pacemakers
flashing traffic lights
automobile turn signals
electronic flash units
Applications:
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Caution: Lowercase (i, q, v) means time-varying.
Instantaneous current i = i(t)
Instantaneous charge q = q(t)
Instantaneous voltage v = v(t)
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Charging a Capacitor
1. idealized battery (or power supply)
constant emf ε (zero internal resistance, r = 0)
2. connecting conductors has negligible resistance
Assumptions:
Initially, capacitor C is uncharged. At t = 0, switch is closed.
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Charging a CapacitorAt t = 0, switch is closed.
vbc = q/C = 0 (since q = 0)
Current Io through the resistor R
ε = IoR
Io = ε/R
After some time t,
Charge q on the capacitor increases.
Current i decreases.
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Charging a CapacitorAfter some time t,
Current i decreases.
Charge q on the capacitor increases.
Kirchhoff’s Loop Rule:
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Charging a Capacitor
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Time Constant τmeasure of how quickly a capacitor charges
If τ is small, capacitor charges quickly.
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Time Constant
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Time Constant
Discharging a CapacitorInitially, capacitor is charged (q = Qo).
1. Remove the battery from RC circuit.
2. Connect point a and c to an open switch.
At t = 0, switch is closed.
Kirchhoff’s Loop Rule:
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Discharging a CapacitorAfter some time t,
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Discharging a CapacitorAfter some time t,
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A 4.60-μF capacitor that is initially uncharged is connected in series with a
7.50-kΩ resistor and an emf source with ε = 125 V and negligible internal
resistance. Just after the circuit is completed, what are
(a) the voltage drop across the capacitor;
(b) the voltage drop across the resistor;
(c) the charge on the capacitor;
(d) the current through the resistor;
(e) the time constant?
(f) A long time after the circuit is completed (after many time constants)
what are the values of the quantities in parts (a)-(d)?
Example:
C
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