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1. Chapter 23 Series and Parallel Circuits
2. 23.1 Simple Circuits A circuit in which all current travels through each device, is called a series circuit.
Two lamps in series are dimmer than one on its own.
The battery pushes the current through the lamps. The more lamps there are, the harder it is for the current to flow. There is more resistance in the circuit. (I = V/R)
3. We can make the lamps brighter again using a battery with a bigger voltage, now the battery is pushing the current harder.
The increase in voltage provided by the batteries or other energy source, Vsource, is equal to the sum of voltage drops across the lamps A an B.
Vsource = VA + VB
The current, I, through the lamps is the same, VA = IRA and VB = I RB. Therefore, Vsource = IRA + I RB or Vsource = I(RA + RB).
The current through the circuit is:
RA + RB
4. Equivalent Resistance (or total resistance) for Resistors in Series RT= RA + RB + ?.
5. Example Problem Voltage Drops in a Series Circuit
Two resistors, 47.0 O and 82.0- O, are connected in series across a 45.0-V battery.
What is the current in the circuit?
What is the voltage drop across each resistor?
The 47.0- O resistor is replaced by a 39.0- O resistor. Will the current increase, decrease, or remain the same?
What will happen to the voltage drop across the 82.0- O resistor?
6. Parallel Circuits A circuit in which there are several current paths is called a parallel circuit.
7. The total resistance in a parallel circuit is always less than any of the branch resistances. Adding more parallel resistances to the paths causes the total resistance in the circuit to decrease. As you add more and more branches to the circuit the total current will increase.
10. Example Problem Equivalent Resistance and current in a Parallel Circuit
Three resistors, 60.0O, 30.0 O, and 20.0 O, are connected in parallel across a 90.0-V battery.
Find the current through each branch of the circuit.
Find the equivalent resistance of the circuit.
Find the current through the battery.
11. The brightness of a light bulb is proportional to the power dissipated by it.
The resistance of a 60-W bulb is higher than that of the 100-W bulb. But, when the bulbs are connected in series, the current through the two bulbs is the same, so P =I2R.
The higher-resistance lamp, the 60-W lamp, now dissipate more power and glows brighter than the 100-W lamp.
12. 23.2 Applications of Circuits Safety Devices
Such as fuses and circuit breakers prevent circuit overloads that can occur when too many appliances are turned on at the same time.
Appliances connected in parallel reduce the equivalent resistance in the circuit and cause more current through the wires. The additional current may produce enough thermal energy (P=I2R) to melt insulation on the wires and cause a short circuit in the wires or even a fire.
13. Fuse: is a short piece of metal that melts and break the circuit if a too large current passes through it.
Circuit breaker: is an automatic switch that opens when the current reaches some set value and thereby stop all current.
14. Circuit Breaker
15. Series-Parallel Circuit
16. Example Problem A hair dryer with a resistance of 12.0 O and a lamp with a resistance of 125 O are connected in parallel to a 125-V source through a 1.5- O resistor in series.
Find the current through the lamp when the hair dryer is off.
Find the current when the hair dryer is on.
Explain why the lamp dims when the hair dryer is on.
18. Voltmeter is used to measure the voltage drop across some part of a circuit. You need to connect the voltmeter in parallel with the resistor.
Should have very high resistance so that it causes the smallest possible change in currents or voltages in the circuit.