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Parallel Circuits: Finding Total Resistance, Current and Missing Readings, Study notes of Physics

Solutions to parallel circuit problems involving finding total resistance, current passing through each resistor, and missing readings. It includes calculations for various resistor combinations and voltage inputs.

What you will learn

  • How to find the missing readings in a parallel circuit?
  • How to find the total resistance in a parallel circuit?
  • What is the current passing through each resistor in a parallel circuit?

Typology: Study notes

2021/2022

Uploaded on 09/12/2022

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Parallel Circuits
Solutions to p 126b,c
1. Find the total resistance in each case.
a. 21
21
21
Rt = [R1-1 + R2-1 + R3-1]-1 = [21-1 + 21-1 + 21-1]-1 = 7.
b. 5
10
20
Rt = [R1-1 + R2-1 + R3-1]-1 = [5-1 + 10-1 + 20-1]-1 = 2.9 .
pf3
pf4
pf5

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Parallel Circuits Solutions to p 126b,c

  1. Find the total resistance in each case. a. 21 Ω

Rt = [R 1 -1^ + R 2 -1^ + R 3 -1^ ]-1^ = [21-1^ + 21 -1^ + 21 -1^ ]-1^ = 7Ω.

b. 5 Ω

Rt = [R 1 -1^ + R 2 -1^ + R 3 -1^ ]-1^ = [5-1^ + 10 -1^ + 20 -1^ ]-1^ = 2.9 Ω.

c. 100 Ω

Rt = [R 1 -1^ + R 2 -1^ + R 3 -1^ ]-1^ = [100-1^ + 50 -1^ + 100 -1^ ]-1^ = 25 Ω.

  1. Find the current passing through each resistor.

a. 12 Ω

120V

Since voltage is constant in parallel, I 1 = V/R 1 = 120/12 = 10A I 2 = V/R 2 = 120/12 = 10A I 3 = V/R 3 = 120/12 = 10A

40 Ω R 1 40 Ω

20 V

R 2

A

What is the current intensity ( I ) flowing through the ammeter?

I = 20/40 = 0.50 A

  1. The following diagram shows a parallel circuit consisting of three resistors.

R (^1)

R (^2)

R (^3)

R 2 = 6 Ω

I 2 = 2 A

R = 3 Ω

I 1 = 4 A

R =?

I 3 = 6 A

1 3

What is the value of resistor R 3?

Since voltage is always constant in parallel, V = 3(4) or (6)(2) = 12V. R 3 = 12V/6A = 2 Ω.

  1. An electrical circuit consists of a power source, two switches (S 1 and S 2 ) and two light bulbs (L 1 and L 2 ). The following table shows what happens to both light bulbs:

Switch Light Bulb

S 1 S 2 L 1 L 2

open open out out

closed open bright out

Which of the following circuit diagrams illustrates the results shown in the table above?

A) C)

B) D)