DC Circuits Real Batteries and Light Bulbs Batteries

DC Circuits Real Batteries and Light Bulbs

Batteries and Terminal Voltage Batteries consist of plates that are charged by a chemical reaction taking place between the plates. The reaction provides the energy to lift charges from a low potential to a high potential. The emf created by the chemical reaction is a potential difference that drives electrical devices attached to the battery. Like other sources of power batteries are not 100% efficient. ++ ++ Reaction −− −−

Batteries and Terminal Voltage Batteries are made of conducting material and thus have resistance. The resistance inside a battery is called the internal resistance r. ++ ++ The emf of the battery is a theoretical potential that would be reached if there were no resistance. −− −− The actual potential produced by a battery is less than the emf due to the loss created by the internal resistance. The actual potential is called the terminal voltage. Reaction

Batteries and Terminal Voltage The terminal voltage is the potential difference between the terminals (ends) of a battery. ++ ++ Reaction V ε I r Terminal voltage emf Current in battery Internal Resistance If the internal resistance is negligible (often the case in most problems) −− −−

Graph of Terminal Voltage The equation for terminal voltage is linear. To determine the exact look of the graph simply rearrange the equation to match y = mx + b. If asked for the voltage vs. current graph of a battery ε V −r The y-intercept is emf The slope is negative The slopes value is the internal resistance. I

Example 3 A battery has an emf of 6. 0 V and an internal resistance of 0. 10 Ω. Determine the terminal voltage if a 3. 0 A current runs through the battery.

When Internal Resistance is Negligible Unless told otherwise: Internal resistance is negligible, r = 0 When working with batteries Ohm’s Law and the power equations modify as follows

Household Wiring Homes are wired in parallel. When you turn lights or appliances on and off the other lights in your house do not get brighter or dimmer. If one light goes out the others remain lit. This is because they are on different parallel circuits.

Household Wiring However, there is a down side. As each new device is turned on you use more and more power increasing the amount of current flowing in the wires. Flowing currents involve collisions and these generate heat. The wires can become hot enough to start a fire. Therefore, one device in the circuit is wired in series. Circuit Breakers (in some circuits fuses are used) Circuit breakers and fuses are a devices that turns the current off if the circuit is overloaded.

Light Bulbs in Circuits Light bulbs are sold by their wattage which is related to the power consumption of the bulb, and we buy lights with a higher wattage to get brighter lights. Light bulbs sold in the USA are intended for a 120 V parallel circuit, and in these circuits higher wattage means brighter bulbs. However, if you wire the same bulbs in series, or use then in European 240 V circuits, you will not draw the wattage stamped on the bulb. Wattage is not fixed! Light bulbs are actually resistors, and it is their resistance that follows the bulb from circuit to circuit. Find the resistance and transfer this to each new circuit.

Light Bulbs in Circuits A 120 W light and 240 W light are connected into a USA 120 V parallel circuit. Power adds. V I R P ε 120 3 40 360 L 1 120 120 L 2 120 2 60 240 V I R P Parallel: voltage stays the same. Use P = IV to find current. Use V = IR to find resistance The resistance of RL 1 and RL 2 are the constant property. This property moves to other circuits ε 120 L 1 120 L 2 60

Light Bulbs in Circuits Connect the same light into a 120 V series circuit. Find total resistance V I R P ε 120 3 40 360 L 1 120 120 L 2 120 2 60 240 V I R P Use V = IR to find the total current. In series current stays the same. Use V = IR to find voltage. Use P = IV to find power. 80 ε 120 0. 67 180 L 1 80 0. 67 120 53. 3 L 2 40 0. 67 60 26. 7 V I R P Power in series does not match the power printed on the bulb. ε Resistance is the only constant. L 1 120 L 2 60 240 40

Light Bulbs in Circuits Now the bulbs are connected in a 240 V parallel circuit. Find total resistance. V I R P ε 120 3 40 360 L 1 120 120 L 2 120 2 60 240 V I R P Use V = IR to find total current Parallel: voltage stays the same. ε 120 0. 67 180 Use V = IR to find current. L 1 80 0. 67 120 53. 3 L 2 40 0. 67 60 26. 7 V I R P ε 240 6 40 1440 L 1 240 2 120 480 L 2 240 4 60 960 Use P = IV to find power. Let’s compare power and resistance for all three scenarios. 80

Light Bulbs in Circuits V I R P What is the same for the light bulbs no matter what circuit they are in? L 1 120 Resistance L 2 60 240 R P The printed wattage on light bulbs is only true if used in a 120 V parallel circuit. In a series circuit the light labeled 240 W actually drew half the power of the 120 W light. To avoid wrong answers find the resistance of a light and then find the true power used. 120 V parallel ε V I 120 V series ε L 1 120 53. 3 L 2 60 26. 7 R P V ε I 240 V parallel L 1 120 480 L 2 60 960