Transcript Direct Current Circuits

Rumus yang dipakai
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Current and Resistance
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Electric Current
• Charges in motion through an area A. The time rate at which charge
flows through the area is defined as the current I. The direction of the
current is the direction in which positive charges flow when free to do
so.
• The SI unit of current is the ampere (A):
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Resistance
• Ohm’s law
• A current density J and an electric field E are established in a
conductor whenever a potential difference is maintained across the
conductor. In some materials, the current density is proportional to
the electric field:
• where the constant of proportionality σ is called the conductivity of
the conductor
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The inverse of conductivity is
resistivity ρ:
Resistance of a uniform
material along the length l
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Resistance and Temperature
• Resistivity versus temperature for a metal
such as copper. The curve is linear over a
wide range of temperatures, and ρ
increases with increasing temperature. As
T approaches absolute zero (inset), the
resistivity approaches a finite value ρ0.
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Electrical Power
• A circuit consisting of a resistor of resistance R and a battery having
a potential difference ΔV across its terminals. Positive charge flows
in the clockwise direction.
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Quick Quiz
• The same potential difference is applied to the
two lightbulbs shown in figure. Which one of the
following statements is true?
– (a) The 30-W bulb carries the greater current and has
the higher resistance.
– (b) The 30-W bulb carries the greater current, but the
60-W bulb has the higher resistance.
– (c) The 30-W bulb has the higher resistance, but the
60-W bulb carries the greater current.
– (d) The 60-W bulb carries the greater current and has
the higher resistance.
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example
• An electric car is designed to run off a bank of 12.0-V batteries with
total energy storage of 2.00 x 107 J.
– (a) If the electric motor draws 8.00 kW, what is the current delivered to the
motor?
– (b) If the electric motor draws 8.00 kW as the car moves at a steady speed of
20.0 m/s, how far will the car travel before it is “out of juice”?
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Kuat Arus
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Resistansi
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Daya
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Direct Current
Circuits
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Rumus yang dipakai
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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.
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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
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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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example
• 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.
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RC Circuits
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.
A capacitor in series with
a resistor, switch, and battery.
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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 with
the 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)
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TERIMA KASIH
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