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20.1 Series and Parallel Circuits In series circuits, current can only take one path. The amount of current is the same at all points in a series circuit. 20.1 Adding resistances in series Each resistance in a series circuit adds to the total resistance of the circuit. Rtotal = R1 + R2 + R3... Total resistance (ohms) Individual resistances (W) 20.1 Series and Parallel Circuits In parallel circuits the current can take more than one path. Because there are multiple branches, the current is not the same at all points in a parallel circuit. Voltage and Current in a Parallel Circuit In a parallel circuit the voltage is the same across each branch because each branch has a low resistance path back to the battery. The amount of current in each branch in a parallel circuit is not necessarily the same. The resistance in each branch determines the current in that branch. 20.1 Advantages of parallel circuits Parallel circuits have two big advantages over series circuits: 1. Each device in the circuit sees the full battery voltage. 2. Each device in the circuit may be turned off independently without stopping the current flowing to other devices in the circuit. 20.1 Adding resistance in parallel circuits A circuit contains a 2 ohm resistor and a 4 ohm resistor in parallel. Calculate the total resistance of the circuit. 20.2 Three circuit laws 20.2 Voltage divider A circuit divides any supplied voltage by a ratio of the resistors. V0 = Output voltage (volts) R1 Vi R1 + R2 resistor ratio (W) Input voltage (volts) 20.2 Solving circuit problems 1. 2. 3. Identify what the problem is asking you to find. Assign variables to the unknown quantities. Make a large clear diagram of the circuit. Label all of the known resistances, currents, and voltages. Use the variables you defined to label the unknowns. You may need to combine resistances to find the total circuit resistance. Use multiple steps to combine series and parallel resistors. 20.3 Alternating and direct current The current from a battery is always in the same direction. One end of the battery is positive and the other end is negative. The direction of current flows from positive to negative. This is called direct current, or DC. 20.3 Alternating and direct current If voltage alternates, so does current. When the voltage is positive, the current in the circuit is clockwise. When the voltage is negative the current is the opposite direction. This type of current is called alternating current, or AC. 20.2 Solving circuit problems 4. 5. 6. If you know the total resistance and current, use Ohm’s law as V = IR to calculate voltages or voltage drops. If you know the resistance and voltage, use Ohm’s law as I = V ÷ R to calculate the current. An unknown resistance can be found using Ohm’s law as R = V ÷ I, if you know the current and the voltage drop through the resistor. Use Kirchhoff’s current and voltage laws as necessary. 20.2 Solving circuit problems A bulb with a resistance of 1Ω is to be used in a circuit with a 6-volt battery. The bulb requires 1 amp of current. If the bulb were connected directly to the battery, it would draw 6 amps and burn out instantly. To limit the current, a resistor is added in series with the bulb. What size resistor is needed to make the current 1 amp? 20.2 Network circuits In many circuits, resistors are connected both in series and in parallel. Such a circuit is called a network circuit. There is no single formula for adding resistors in a network circuit. For very complex circuits, electrical engineers use computer programs that can rapidly solve equations for the circuit using Kirchhoff’s laws. 20.2 Calculate using network circuits Three bulbs, each with a resistance of 3Ω, are combined in the circuit in the diagram Three volts are applied to the circuit. Calculate the current in each of the bulbs. From your calculations, do you think all three bulbs will be equally bright? 20.3 Power Voltage (volts) Power (watts) P = VI Current (amps) 20.3 Calculate power A light bulb with a resistance of 3Ω is connected to a 1.5volt battery in the circuit shown at right. Calculate the power used by the light bulb. 20.3 Paying for electricity Electric companies charge for the number of kilowatt-hours used during a set period of time, often a month. One kilowatt-hour (kWh) means that a kilowatt of power has been used for one hour. Since power multiplied by time is energy, a kilowatt-hour is a unit of energy. One kilowatt-hour is 3.6 x 106 joules. 20.3 Calculate power Your electric company charges 14 cents per kilowatt-hour. Your coffee maker has a power rating of 1,050 watts. How much does it cost to use the coffee maker one hour per day for a month? 20.3 Alternating and direct current AC current is used for almost all high-power applications because it is easier to generate and to transmit over long distances. The 120 volt AC (VAC) electricity used in homes and businesses alternates between peak values of +170 V and 170 V at a frequency of 60 Hz. AC electricity is usually identified by the average voltage, (120 VAC) not the peak voltage. Application: Wiring in Homes and Buildings Application: Wiring in Homes and Buildings