Everything Science Grade 10

CHAPTER 17. ELECTRIC CIRCUITS 17.5

Step 2:Apply the relevant principles

The total resistance for resistors in parallel has been given as

1

RP =

1

R 1 +

1

R 2 +...

. We have three resistors and we now the resistances. In this case we
have that:
1
RP=

1

R 1 +

1

R 2 +...

there are three resistors

1

RP=

1

R 1 +

1

R 2 +

1

R 3

add the fractions

1

RP=

1

R 1 ×

R 2 R 3

R 2 R 3 +

1

R 2 ×

R 1 R 3

R 1 R 3 +

1

R 3 ×

R 1 R 2

R 1 R 2

1

RP=

R 2 R 3

R 1 R 2 R 3 +

R 1 R 3

R 1 R 2 R 3 +

R 1 R 2

R 1 R 2 R 3

rearrange

1

RP=

R 2 R 3 +R 1 R 3 +R 2 R 3

R 1 R 2 R 3

RP=R R^1 R^2 R^3

2 R 3 +R 1 R 3 +R 2 R 3

RP=(7 Ω)(3 Ω) + (15 Ω)(3 Ω) + (7 Ω)(15 Ω)(15 Ω)(7 Ω)(3 Ω)

RP= 315 Ω

3

21 Ω^2 + 45 Ω^2 + 105 Ω^2

RP=315 Ω

3

171 Ω^2

RP= 1,84 Ω

Step 3:Quote the final result

The total resistance of the resistors in parallel is 1 ,84 Ω. It makes sense

that this is less than in the previous example because we added an

additional path and reduced the overall resistance in the circuit.

When calculating the resistance for complex resistor configurations, you can start with any
combination of two resistors (in series or parallel) and calculate their total resistance. Then
you can replace them with a single resistor that has the total resistance you calculated.
Now use this new resistor in combination with any other resistor and repeat the process
until there is only one resistor left. In the above example we could just have used the
answer from the first example in parallel with the new resistor and we would get the same
answer.

Physics: Electricity and Magnetism 307