Resistors and Ohm’s Law

What is Resistance? Resistance: Property of a substance that slow down the movement of electrons and converts electrical energy into other forms Unit is the Ohm (Ω) An ohmmeter measures resistance Used to reduce current flow. They are passive components, meaning they only consume power (and can't generate it).

Resistors A resistor is an electrical component that restricts the flow of electric current. Resistors are used to control current and voltage to suit the needs of the other electrical devices in a circuit. Symbol: Many resistors are made of carbon, a semiconductor.

How does resistance come into play in a light bulb? The filament in a light bulb is a thin wire which has resistance to the flow of electricity. As a result, the filament heats up and starts glowing due to the gas inside the bulb, converting electrical energy to light energy (and heat). Tungsten wire has 400x more resistance than copper wire. Electricity flows through a thin wire in the light bulb called the filament. The filament used in a bulb has a property called "resistance." ... A filament has a lot ofresistance to electricity. Therefore as a result of this, the filament heats up and starts glowing, converting electrical energy to light energy. Resistance is the amount of friction that an object will put against electricity flowing through it. A filament has a lot of resistance to electricity. Therefore as a result of this, the filament heats up and starts glowing, converting electrical energy to light energy. This is because of the Joule-effect, which means that resistances heat up when electrical current runs through them.

How is Resistance related to voltage and current? Current is the movement of electrons (charge) though a conductor Voltage is what makes electrons move through conductor Resistance works against and slows down motion of electrons Good conductors have low resistance, so electrons flow through them easily Poor conductors have high resistance, so electrons are slowed down. (good insulators)

Ohm’s Law: The potential difference (voltage) across a conductor is proportional to the current through it. V = I R where V is the potential difference between two points which include a resistance R.

We can rewrite the equation

Ohm’s Law: The current flowing through a resistor is directly proportional to the potential difference across it. It is an equation showing how voltage, current and resistance are related.

Resistors in Series When resistors are arranged in a series, the current has only one path to take and is the same through each resistor. The total resistance of the circuit is found by adding up the individual resistors: R = R1 + R2 + R3 + ...

Resistors in Parallel The combined resistance of two or more resistors is less than that of either resistor by itself.

Resistors in Parallel When resistors are connected in parallel, the supply current is equal to the sum of the currents through each resistor. In other words the currents in the branches of a parallel circuit add up to the supply current. When resistors are connected in parallel, they have the same potential difference across them.

In a SERIES Circuit: IT = I1 = I2 = I3 …. VT = V1 + V2 + V3 …. Current: SAME through whole circuit IT = I1 = I2 = I3 …. Voltage: voltage across loads ADD UP to TOTAL VOLTAGE VT = V1 + V2 + V3 …. Resistance: Resistors INCREASE total resistance in circuit  TOTAL CURRENT DECREASES in circuit as resistors are ADDED. RT = R1 + R2 + R3 ….

In Parallel Circuits: IT = I1 +I2 + I3 …. Current through each path ADDS UP to Total current IT = I1 +I2 + I3 …. Voltage: is the SAME across each load as total voltage VT = V1 = V2 = V3 …. Resistance: Resistors DECREASE total resistance in circuit  TOTAL CURRENT INCREASES in circuit as resistors are ADDED.

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Practice Problems p322 HW: CYU p 319 #1,2, 3, 4, 7, 9 WB p124 -127 (BC Sc 9) Probe WB p

With a 10 V battery, by V = I R the total current in the circuit is: I = V / R = 10 / 20 = 0.5 A The current through each resistor would be 0.5 A.

Series and Parallel Circuits A series circuit is an electric circuit that has only one path for electrons to flow. Electricity cannot go to just one electrical device, it must flow through all devices All loads in a circuit share the electric pressure (voltage). If you add electric loads, each one get less electric pressure (light bulbs will dim as more are added) We use series circuits in: Computers, radios, TV’s, rockets

Resistors in Parallel When resistors are arranged in parallel, the current breaks up, with some flowing along each parallel branch and re-combining when the branches meet again. (The voltage across each resistor in parallel is the same) The total resistance is found by adding up the reciprocals of the resistance values, and then taking the reciprocal of the total: equivalent resistance of resistors in parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R3 +...

VT = 9V VT = V 1 + V2 + V3 Lamp 1 = 6V @ 1A lamp 2 = 12V @ 0 VT = 9V VT = V 1 + V2 + V3 Lamp 1 = 6V @ 1A lamp 2 = 12V @ 0.5 A lamp 3 = 9 Suppose you had three lamps - each has a different working voltage and takes a different current. What would happen if I connected all three in series and connected them to a 9V battery.

V1 + V2 = VT 2 V + 4V = 6 V I1 = I2 = IT 0.5 A = 0.5 A = 0.5 A Voltmeter shows

Check your Understanding a. Two 3-Ω resistors placed in series would provide a resistance that is equivalent to one _____-Ω resistor. b. Three 3-Ω resistors placed in series would provide a resistance that is equivalent to one _____-Ω resistor. c. Three 5-Ω resistors placed in series would provide a resistance that is equivalent to one _____-Ω resistor. d. Three resistors with resistance values of 2-Ω , 4-Ω , and 6-Ω are placed in series. These would provide a resistance that is equivalent to one _____-Ω resistor. e. Three resistors with resistance values of 5-Ω , 6-Ω , and 7-Ω are placed in series. These would provide a resistance that is equivalent to one _____-Ω resistor. f. Three resistors with resistance values of 12-Ω, 3-Ω, and 21-Ω are placed in series. These would provide a resistance that is equivalent to one _____- Ω resistor. Req = R1 + R2 + R3 + ...a. Two 3-Ω resistors placed in series would provide a resistance which is equivalent to one 6-Ω resistor. b. Three 3-Ω resistors placed in series would provide a resistance which is equivalent to one 9-Ω resistor. c. Three 5-Ω resistors placed in series would provide a resistance which is equivalent to one 15-Ω resistor. d. Three resistors with resistance values of 2-Ω , 4-Ω , and 6-Ω are placed in series. These would provide a resistance which is equivalent to one 12-Ω resistor. e. Three resistors with resistance values of 5-Ω , 6-Ω , and 7-Ω are placed in series. These would provide a resistance which is equivalent to one 18-Ω resistor. f. Three resistors with resistance values of 12-Ω , 3-Ω , and 21-Ω are placed in series. These would provide a resistance which is equivalent to one 36-Ω resistor.

2. As the number of resistors in a series circuit increases, the overall resistance __________ (increases, decreases, remains the same) and the current in the circuit __________ (increases, decreases, remains the same). As the number of resistors in a series circuit increases, the overall resistance increases and the current in the circuit decreases. close

3. Make comparisons of the voltage and the current at the designated points for each diagram. The conventional current is directed through the external circuit from the positive terminal to the negative terminal. The magnitude of this current (I) is everywhere the same - thus the equal sign in the current comparisons. As charge progresses in the direction of the conventional current, there is a drop in electric potential every time it passes through a light bulb. By the time the charge reaches the negative terminal, its electric potential has dropped to zero volts. The closer a position is to the positive terminal, the higher its potential; and conversely, the closer a position is to the negative terminal, the lower its potential. If two locations are separated by a mere wire (such as location D and F in Diagram B), then their potential is approximately the same since there is relatively little resistance in a wire.  

Answer

All three bulbs will have the same brightness. 4. Three identical light bulbs are connected to a D-cell as shown at the right. Which one of the following statements is true? All three bulbs will have the same brightness. The bulb between X and Y will be the brightest. The bulb between Y and Z will be the brightest. The bulb between Z and the battery will be the brightest. Answer: A The current in a series circuit is the same at each resistor present in the circuit. Since each light bulb has the same resistance ("identical bulbs") and the same current, they will have the same power output (P = I2R as discussed in the previous Lesson ). Thus, they will shine with the same brightness

a. Increase the resistance of one of the bulbs. 5. Three identical light bulbs are connected to a battery as shown at the right. Which adjustments could be made to the circuit that would increase the current being measured at X? List all that apply. a. Increase the resistance of one of the bulbs. b. Increase the resistance of two of the bulbs. c. Decrease the resistance of two of the bulbs. d. Increase the voltage of the battery. e. Decrease the voltage of the battery. f. Remove one of the bulbs. Answer: C, D, and F The current at location X is the same as the current at the battery location. To increase the value of the current at the battery, it would be necessary to increase the battery voltage (choice D) or to decrease the equivalent resistance. Since the equivalent resistance is the sum of the resistance of the individual resistors, any decrease of resistance or removal of a resistor will lead to a decrease in the equivalent resistance.

6. Three identical light bulbs are connected to a battery as shown at the right. W, X,Y and Z represent locations along the circuit. Which one of the following statements is true? a) The potential difference between X and Y is greater than that between Y and Z. b. The potential difference between X and Y is greater than that between Y and W. c. The potential difference between Y and Z is greater than that between Y and W. d. The potential difference between X and Z is greater than that between Z and W. e. The potential difference between X and W is greater than that across the battery. f. The potential difference between X and Y is greater than that between Z and W.   Answer: D In a series circuit, the current is the same at each resistor. If the light bulbs are identical, then the resistance is the same for each resistor. The voltage drop (I•R) will be the same for each resistor since the current at and the resistance of each resistor is the same. Thus the electric potential difference across any one of the bulbs will be the same as that across any one of the other bulbs. And the electric potential difference across two or three bulbs will be greater than that across one bulb. The voltage boost in the battery will be equal to the sum of the voltage drops across all three resistors. Only choice D meets these criteria.

7. Compare circuit X and Y below. Each is powered by a 12-volt battery 7. Compare circuit X and Y below. Each is powered by a 12-volt battery. The voltage drop across the 12-ohm resistor in circuit Y is ____ the voltage drop across the single resistor in X a. smaller than b. larger than c. the same as Answer: A The voltage gained at the battery is equal to the accumulative voltage drop when passing through the external circuit. In circuit X, the voltage drop across the single resistor must be 12 V. In circuit Y, the voltage drop across the 12 ohm resistor must be less than 12 V since there will be an additional voltage drop in the 6 ohm resistor. In fact, one might reason that the two voltage drops in circuit Y will be 8 volts and 4 volts respectively, to add to a total voltage drop of 12 volts.