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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 (inthis case, a battery), of internalresistance r, connected to anexternal 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

• 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 fora 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 fora 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 connectionsand back to ground through the neutral wire. In the situation shown, the live wire hascome into contact with the drill case. As a result, the person holding the drill acts as acurrent 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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