Parallel Circuit Resistance Equivalent Resistance for Resistors in Parallel: Equivalent Resistance for Resistors in Parallel: 1 / R = 1 / R1 + 1 / R2 + 1 / R Three resistors, 60 Ω, 30 Ω, 20 Ω, are connected in parallel across a 90V battery. a) Draw a schematic b) Find the current through each branch of the circuit c) Find the equivalent resistance of the circuit d) Find the current through the battery

Answers a)b) 1.5A, 3A, 4.5A c) R eff = 10Ω d) I = 90V/10Ω = 9A

More Practice A circuit contains six 240-Ω lamps (60-W bulbs) and a 10.0-Ω heater connected in parallel. The voltage across the circuit is 120V. What is the current in the circuit… A circuit contains six 240-Ω lamps (60-W bulbs) and a 10.0-Ω heater connected in parallel. The voltage across the circuit is 120V. What is the current in the circuit… a) when four lamps are turned on? b) when all lamps are on? c) when six lamps and the heater are operating?

Answers a) 2A b) 3A c) 15A ** **Note that the current changes so drastically when the 10.0 Ω heater is on because its the path of least resistance (how poetic)…more coulombs can move through the circuit every second (C/s = A) because there is a path to take with little resistance working against them. Woot! Woot!

Series vs. Parallel Think of equivalent resistance like cars on a highway. On a single lane highway with few exits (series), a car crash (resistance) up ahead affects every car on the highway. All cars have to pass that point so rate of movement (cars/second or C/s) slows down. However, if there are several lanes or exits you can follow to get out of the traffic and get to the same place, wouldnt you use them? Well, so would charged particles! The car crash will effect your rate less if you have another path you can take. Especially if the other cars are also taking alternate routes. Fewer cars per area = less traffic… or in our case less effective resistance! Think of equivalent resistance like cars on a highway. On a single lane highway with few exits (series), a car crash (resistance) up ahead affects every car on the highway. All cars have to pass that point so rate of movement (cars/second or C/s) slows down. However, if there are several lanes or exits you can follow to get out of the traffic and get to the same place, wouldnt you use them? Well, so would charged particles! The car crash will effect your rate less if you have another path you can take. Especially if the other cars are also taking alternate routes. Fewer cars per area = less traffic… or in our case less effective resistance!

Series Parallel