Resistors in Series and Parallel

Resistors in Series and Parallel

By Rachel Wampler

• Circuit forms one "loop"

• ​Multiple devices in the circuit

• Same current through each device​

• A break in the loop means no more flowing current

• The resisters divide the voltage between them ​

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Series Wiring

Voltage Divide Among Resistors

Multiple Choice

A 5.17 kΩ reistor and a 10.09 kΩ resistor are connected in series.

What is the equivalent resistance?

• 52.17 kΩ

• 15.26 kΩ

• 4.92 kΩ

• 1.95 kΩ

Multiple Choice

Bathroom vanity lights are occasionally wired in series. V=120V and you install three bulbs with R=8Ω and one bulb with R=12Ω. what is the current, voltage of each bulb, and the total power?

• I = 3.33 A

  V = 26.7 V , 40 V

  P = 400 W

• I = 5 A

  V = 40 V, 60 V

  P = 900 W

• I = 10 A

  V = 80 V, 120 V

  P = 3600 W

• I = 2880 A

  V =23 kV, 35 kV

  P = 299 MW

• The same voltage across several devices

• Houses are typically wired in parallel

• A fault in a device has no effect on current

• Resistors divide current​

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Parallel Wiring

Parallel Derivation

Parallel Formula Derivation

Multiple Choice

A 1000 Ω resistor and 101 Ω resistor are connected in parallel. What is the equivalent resistance? If they were connced to a 3 V battery, how much total current would the battery supply? How much current goes through each resistor?

• R_p = 91.8 Ω

  I_total = 32.7 mA

  I = 3.0mA, 29.7mA

• R_p = 1105 Ω

  I_total = 32.7 mA

  I = 3.0mA, 29.7mA

• R_p = 91.8 Ω

  I_total = 32.7 mA

  I = 5.0mA, 29.7mA

• R_p = 1105 Ω

  I_total = 32.7 mA

  I = 5.0mA, 29.7mA

1. Simplify any series portions of each branch

2. simplify the parallel circuity of the branches

3. If necessary simplify remaining series​

Circuits Wired in Series and Parallel

Multiple Choice

find the equivalent resistance and the total current of the following circuit.

• R = 15260 Ω

  I = 196 mA

• R = 13255 Ω

  I = 226 mA

• R = 100900 Ω

  I = 297 mA

• R = 14360 Ω

  I = 209 mA

Multiple Choice

Find the equivalent resistance.

• 3826.5 Ω

• 3927 Ω

• 994.1 Ω

• 6164.1 Ω