Circuits Chapter 35

Series In series circuits, current can only take one path. The amount of current is the same at all points in a series circuit.

Resistance in a Series Circuit Each resistance in a series circuit adds to the total resistance of the circuit. Rtotal = R1 + R2 + R3... Total resistance (ohms) Individual resistances (W)

Calculating Resistance Light bulbs, resistors, motors, and heaters usually have much greater resistance than wires and batteries.

Each separate resistance creates a voltage drop as the current passes through. As current flows along a series circuit, each type of resistor transforms some of the electrical energy into another form of energy Ohm’s law is used to calculate the voltage drop across each resistor.

Resistance in Parallel Circuit 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.

Parallel Circuits Sometimes these paths are called branches. The current through a branch is also called the branch current. When analyzing a parallel circuit, remember that the current always has to go somewhere. The total current in the circuit is the sum of the currents in all the branches. At every branch point the current flowing out must equal the current flowing in. This rule is known as Kirchhoff’s current law.

Parallel Circuits 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.

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.

Short Circuit A short circuit is a parallel path in a circuit with zero or very low resistance. Short circuits can be made accidentally by connecting a wire between two other wires at different voltages. Short circuits are dangerous because they can draw huge amounts of current.

Calculating Resistance in Parallel 1) You are asked for the resistance. 2) You are given the circuit diagram and resistances. 3) Use the rule for parallel resistances. 4) Solve: 1/R total = 1/2 Ω + 1/4 Ω = 2/4 Ω +1/4 Ω = 3/4 Ω R= 4/3 Ω = 1.33 Ω A circuit contains a 2 ohm resistor and a 4 ohm resistor in parallel. Calculate the total resistance of the circuit.

Network Circuits Key Question: How do we analyze network circuits?

Network Circuits All circuits work by manipulating currents and voltages. The process of circuit analysis means figuring out what the currents and voltages in a circuit are, and also how they are affected by each other.

Circuit Analysis

Current Calculation 1) You are asked for the current. 2) You are given the voltage and resistance. 3) Use Ohm’s law: I = V ÷ R. 4) For the 3Ω bulb: I = (3 V) ÷ (3 Ω) = 1 A. For the 0.5 Ω bulb: I = (3 V) ÷ (0.5 Ω) = 6 A. The battery must supply the current for both bulbs, which adds up to 7 amps. Two bulbs with different resistances are connected in parallel to batteries with a total voltage of 3 volts. Calculate the total current supplied by the battery.

Identify what the problem is asking you to find 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.

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.

Practice 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? 1) You are asked to calculate the resistance. 2) You are told it is a series circuit and given the voltage, total current, and one resistance. 3) Use Ohm’s law, R = V ÷ I, and add the resistance in series. 4) Solve: Total resistance = 6V ÷ 1A = 6Ω. SInce the bulb is 1Ω, the additional resistor must be 5Ω to get a total 6Ω of resistance.

Summarizing Terms

Calculate power (P = V/I) A light bulb with a resistance of 3Ω is connected to a 1.5- volt battery in the circuit shown at right. Calculate the power used by the light bulb. 1) You are asked to find the power used by the light bulb. 2) You are given the voltage of the battery and the bulb’s resistance. 3) Use Ohm’s law, I = V/R, to calculate the current; then use the power equation, P=VI, to calculate the power. 4) Solve: I = 1.5V ÷ 1.5Ω = 1A P = 1.5V × 1A = 1.5 W; the bulb uses 1.5 watts of electric power.