Aim: How do we analyze a parallel circuit? HW: Problem Set

Review How do we describe current through series resistors? The current through each is the same and equals the total current because there is one loop. How do we describe the voltage across each resistor? The voltage across each resistor is different and adds to the total voltage since both go through a single loop. How do we solve for the equivalent resistance? Equivalent resistance given by straight addition of individual resistors.

Parallel Circuits A circuit in which all of the components are connected “in parallel” to the same voltage source, creating MULTIPLE LOOPS.

Parallel Circuits The charges fall through the 30Ω resistor at a slower rate. Less CURRENT flows through that branch of the circuit!

Parallel Rules The equivalent resistance is the INVERSE OF THE SUM of the INVERSE OF EACH RESISTANCE The total current in the circuit is equal to the SUM of the CURRENT passing through each resistor. The voltage is the same for ALL resistors in the circuit. All COMPONENTS and the WHOLE CIRCUIT obey Ohm’s Law (There are Multiple Loops!)

Junction Rule The total current flowing INTO a junction of two or more wires is the SAME as the total current flowing OUT of the junction. 10A ? 5A 5A

Junction Rule 6A ? ? 10A 6A 4A 2A

Envelope Activity Solve for the magnitude and direction of the current in the unknown wire.

5A 2A 10A 11A 3A ? 6A ? 1A 7A What is the direction and magnitude of current in the unknown wire? What is the direction and magnitude of current in the unknown wire? 9A ? 4A What is the direction and magnitude of current in the unknown wire? 6A

V I R P R1 R2 R3 Req VIRP Chart Example 30 Ω 60 V R3 = 30 Ω 120W 60 V 10 Ω 360W R1 = 30 Ω 60 V

V I R P R1 70 Ω R2 60 Ω R3 50 Ω Req R3 = 50 Ω 0.05 A 2.5 V 0.036A 0.09W 2.5 V 0.042A 0.11 W R2 = 60 Ω 2.5 V 0.05A 0.13 W 2.5 V 0.128A 19.62 Ω 0.32W R1 = 70 Ω *Remember: You need 2/3 variables across a resistor or for the entire circuit in order to use Ohm’s Law! ? V

SUMMARY Describe the Parallel Circuit rules for… Voltage Current Resistance Describe the Junction Rule

AP Styled Questions I have two circuits with identical batteries and bulbs. How does current flow in each circuit? 1 Point

AP Response The series circuit has the same current flow across each resistor because the current flows through a single loop where it is the same across each circuit element. In the parallel circuit the current is half it’s total amount across each element because it is split between multiple loops by the junction rule.

2. Which circuit has more power. Make specific reference to equations 2. Which circuit has more power? Make specific reference to equations. 3 Points

2. Since all of the bulbs and batteries are identical, the bulbs in parallel will be brighter, which means there is more power. In the series circuit current is the same everywhere, but it encounters more resistance than in the parallel one. This can be shown by the following equations. Based on the junction rule there must be more total current in the parallel circuit, so by any power relationship we can see there is also more power.