(A) Find the current in the circuit.
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Transcript (A) Find the current in the circuit.
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Direct Current Circuits:
3-1 EMF
3-2 Resistance in series and parallel .
3-3 Rc circuit
3-4 Electrical instruments
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Example:
(A) Find the current in the circuit.
starting at a, we see that a b
represents a potential difference
of + Ɛ1
b c represents a potential
difference of -IR1,
c d represents a potential
difference of - Ɛ2, and
d a represents a potential
difference of -IR2
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The negative sign for I indicates that the direction of the current is
opposite the assumed direction.
(B) What power is delivered to each resistor? What
power is delivered by the 12-V battery?
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Problem-Solving Strategy – Kirchhoff’s Rules
Draw the circuit diagram and assign labels and
symbols to all known and unknown quantities
Assign directions to the currents.
Apply the junction rule to any junction in the
circuit
Apply the loop rule to as many loops as are
needed to solve for the unknowns
Solve the equations simultaneously for the
unknown quantities
Check your answers
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Example:
A) Under steady-state conditions, find the unknown currents
I1, I2, and I3 in the multiloop circuit shown in Figurev
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(B) What is the charge on the capacitor?
We can apply Kirchhoff’s loop rule to loop bghab
(or any other loop that contains the capacitor) to find the
potential difference ∆Vcap across the capacitor. We use
this potential difference in the loop equation without
reference to a sign convention because the charge on
the capacitor depends only on the magnitude of the
potential difference.
Moving clockwise around this loop, we obtain
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Quiz 3:
In using Kirchhoff’s rules, you generally assign a
separate unknown current to
(a) each resistor in the circuit (b) each loop in the
circuit (c) each branch in the circuit (d) each battery
in the circuit.
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Ans.
(c) each branch in the circuit
A current is assigned to a given branch of a circuit.
There may be multiple resistors and batteries in a given
branch.
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RC Circuits
A direct current circuit may contain capacitors and
resistors, the current will vary with time
When the circuit is completed, the capacitor starts
to charge
The capacitor continues to charge until it reaches
its maximum charge (Q = Cε)
Once the capacitor is fully charged, the current in
the circuit is zero
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Charging Capacitor in an RC Circuit
The charge on the capacitor
varies with time
q = Q(1 – e-t/RC)
The time constant, =RC
The time constant represents
the time required for the charge
to increase from zero to 63.2%
of its maximum
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The following dimensional analysis shows that τ has the
units of time:
The energy output of the battery as the capacitor is fully
charged is Q Ɛ= Ɛ C 2.
After the capacitor is fully charged, the energy stored in
the capacitor is 1/2Q Ɛ = 1/2 CƐ 2, which is just half the
energy output of the battery.
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Notes on Time Constant
In a circuit with a large time constant, the
capacitor charges very slowly
The capacitor charges very quickly if there is a
small time constant
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Discharging Capacitor in an RC Circuit
When a charged capacitor is
placed in the circuit, it can be
discharged
q = Q e-t/RC
The charge decreases
exponentially
At t = = RC, the charge
decreases to 0.368 Qmax
In other words, in one time
constant, the capacitor loses
63.2% of its initial charge
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5- Electric meter
Ammeters and Voltmeters
An ammeter is a device for measuring current, and a
voltmeter measures voltages.
The current in the circuit must flow through the ammeter;
therefore the ammeter should have as low a resistance as
possible, for the least disturbance.
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Ammeters and Voltmeters
A voltmeter measures the potential
drop between two points in a circuit. It
therefore is connected in parallel; in
order to minimize the effect on the
circuit, it should have as large a
resistance as possible.
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Summary
• Power in an electric circuit:
• If the material obeys Ohm’s law,
• Energy equivalent of one kilowatt-hour:
• Equivalent resistance for resistors in series:
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Summary
• Inverse of the equivalent resistance of resistors in series:
• Junction rule: All current that enters a junction must
also leave it.
• Loop rule: The algebraic sum of all potential charges
around a closed loop must be zero.
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Summary
• Equivalent capacitance of capacitors connected in parallel:
• Inverse of the equivalent capacitance of capacitors
connected in series:
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Kirchhoff’s rules:
1- Junction rule. The sum of the currents entering any
junction in an electric circuit must equal the sum of the
currents leaving that junction:
2- Loop rule. The sum of the potential differences across all
elements around any circuit loop must be zero:
The first rule is a statement of conservation of charge; the
second is equivalent to a statement of conservation of energy.
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Note:
When a resistor is traversed in the direction of the current,
the potential difference ∆V across the resistor is -IR.
When a resistor is traversed in the direction opposite the
current, ∆V = +IR.
When a source of emf is traversed in the direction of the emf
(negative terminal to positive terminal), the potential
difference is +Ɛ .
When a source of emf is traversed opposite the emf (positive
to negative), the potential difference is -Ɛ
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• Charging a capacitor:
where Q = C Ɛ is the maximum charge on the capacitor. The
product RC is called the time constant Ƭ of the circuit.
• Discharging a capacitor:
where Q is the initial charge on the capacitor and I0 = Q /RC is
the initial current in the circuit.
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Summary
• Ammeter: measures current. Is connected in series.
Resistance should be as small as possible.
• Voltmeter: measures voltage. Is connected in parallel.
Resistance should be as large as possible.
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Household Circuits
The utility company
distributes electric power
to individual houses with
a pair of wires
Electrical devices in the
house are connected in
parallel with those wires
The potential difference
between the wires is
about 120V
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