direct current circuits - universitas...
TRANSCRIPT
1
Direct Current Circuits
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Electromotive Force
• The emf of a battery is the maximum possible voltage that the battery can provide between its terminals.
Circuit diagram of a source of emf (in
this case, a battery), of internal
resistance r, connected to an
external resistor of resistance R.
Graphical representation showing
how the electric potential changes
as the circuit in part (a) Is traversed
clockwise.
3
Resistors in Series and Parallel
• For a series combination of two resistors, the currents are the same in both resistors because the amount of charge that passes through
R1 must also pass through R2 in the same time interval.
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• the equivalent resistance of a series connection of resistors is the numerical sum of the individual resistances and is always greater
than any individual resistance.
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Quick Quiz
• With the switch in the circuit of figure closed (left), there is no current in R2, because the current has an alternate zero-resistance path
through the switch. There is current in R1 and this current is
measured with the ammeter (a device for measuring current) at the right side of the circuit. If the switch is opened (right), there is current
in R2 . What happens to the reading on the ammeter when the switch
is opened?
– the reading goes up
– the reading goes down
– the reading does not change.
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• when resistors are connected in parallel, the potential differences across the resistors is the same.
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• the inverse of the equivalent resistance of two or more resistors connected in parallel is equal to the sum of the inverses of the
individual resistances. Furthermore, the equivalent resistance is
always less than the smallest resistance in the group.
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example
• A homeowner wishes to install 12-volt landscape lighting in his back yard. To save money, he purchases inexpensive 18-gauge cable, which has a relatively high resistance per unit length. This cable consists of two side-by-side wires separated by insulation, like the cord on an appliance. He runs a 200-foot length of this cable from the power supply to the farthest point at which he plans to position a light fixture. He attaches light fixtures across the two wires on the cable at 10-foot intervals, so the light fixtures are in parallel. Because of the cable’s resistance, the brightness of the bulbs in the light fixtures is not as desired. Which problem does the homeowner have?
– All of the bulbs glow equally less brightly than they would if lower resistance cable had been used.
– The brightness of the bulbs decreases as you move farther from the power supply.
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Kirchhoff’s Rules
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• Rules for determining the potential differences across a resistor and a battery. (The battery is assumed to have no internal resistance.)
Each circuit element is traversed from left to right.
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• A single-loop circuit contains two resistors and two batteries, as shown in figure. (Neglect the internal resistances of the batteries.)
Find the current in the circuit.
example
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RC Circuits
A capacitor in series with
a resistor, switch, and battery.
Circuit diagram representing
this system at time t < 0, before
the switch is closed.
Circuit diagram at time t > 0,
after the switch has been closed.
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• Plot of capacitor charge versus time for the circuit shown in figure before. After a time interval equal to one time constant τ has passed,
the charge is 63.2% of the maximum value Cε The charge
approaches its maximum value as t approaches infinity.
• Charge as a function of time for
a capacitor being charged
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• Plot of current versus time for the circuit shown in figure before. The current has its maximum value I0 =ε/R at t = 0 and decays to zero exponentially as t approaches infinity. After a time interval equal to one time constant τ has passed, the current is 36.8% of its initial value.
• Current as a function of time for
a capacitor being charged
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Discharging a Capacitor
• A charged capacitor connected to a resistor and a switch, which is open for t < 0. After the switch is closed at t = 0, a current that
decreases in magnitude with time is set up in the direction shown,
and the charge on the capacitor decreases exponentially with time.
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• Charge as a function of time for a discharging capacitor
• Current as a function of time for a discharging capacitor
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Electrical Meters
• The galvanometer is the main component in analog meters for
measuring current and voltage.
• The principal components of a
D’Arsonval galvanometer. When the coil
situated in a magnetic field carries a current, the magnetic torque causes the
coil to twist. The angle through which the coil rotates is proportional to the
current in the coil because of the
counteracting torque of the spring.
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The Ammeter
• Ideally, an ammeter should have zero resistance so that the current being measured is not altered.
• Current can be measured with an ammeter connected in series withthe elements in which the measurement of a current is desired.
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The Voltmeter
• An ideal voltmeter has infinite resistance so that no current exists in it.
• The potential difference across a resistor can be measured with a
voltmeter connected in parallel with the resistor
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Household Wiring and Electrical Safety
• Wiring diagram for a household circuit. The
resistances represent
appliances or other electrical devices that operate with an
applied voltage of 120 V.
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A diagram of the circuit for an electric drill with only two connecting wires.
The normal current path is from the live wire through the motor connections
and back to ground through the neutral wire. In the situation shown, the live wire has
come into contact with the drill case. As a result, the person holding the drill acts as a
current path to ground and receives an electric shock.
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This shock can be avoided by connecting the drill case to ground
through a third ground wire. In this situation, the drill case remains
at ground potential and no current exists in the person.
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quiz
• Under steady-state conditions, find the unknown currents I1, I2, and I3 in
the multiloop circuit shown in figure
(873)