Peoples Physics Concepts

13.4. Resistors in Parallel http://www.ck12.org

13.4 Resistors in Parallel

• Analyze and solve problems involving circuits with resistors in parallel.

Students will learn how to analyze and solve problems involving circuits with resistors in parallel.

Key Equations

1

Rtotal

=

1

R 1

+

1

R 2

+

1

R 3

+...

Guidance

Resistors in Parallel:All resistors are connected together at both ends. There are many rivers (i.e. The main river

branches off into many other rivers), so all resistors receive different amounts of current. But since they are all

connected to the same point at both ends they all receive the same voltage.

Example 1

A circuit is wired up with 2 resistors in parallel.

Both resistors are directly connected to the power supply, so both have the same 20V across them. But they are on

different ’rivers’ so they have different current flowing through them. Lets go through the same questions and

answers as with the circuit in series.

Question:What is the total resistance of the circuit?

Answer:Thetotal resistance isRtotal^1 =R^11 +R^12 = 901 Ω+ 101 Ω= 901 Ω+ 909 Ω= 9010 Ωthus,Rtotal=^9010 Ω= 9 Ω

∗Note: Total resistance for a circuit in parallel will always be smaller than smallest resistor in the circuit.

Question:What is the total current coming out of the power supply?

Answer:Use Ohm’s Law(V=IR)but solve for current(I=V/R).

Itotal=

Vtotal

Rtotal

=

20 V

9 Ω

= 2. 2 A

Question:How much power does the power supply dissipate?