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1Dunblane High SchoolRG

What you need to know

Derive the expression for the total

resistance of any number of

resistors in series, by consideration ofthe conservation of energy.

Derive the expression for the totalresistance of any number of

resistors in parallel by consideration ofthe conservation of charge.

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2Dunblane High SchoolRG

Resistors in Series

R1 R3R2RT

EMF EMF

These two circuits have the same effective resistance

The emf = to the sum of the p.d.s around the circuit

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3Dunblane High SchoolRG

Resistors in Series

R1 R3R2RT

VT EMF

IRT = IR1 + IR2 + IR3But in a series circuit the current is the same at all

points so we can divide by I so.RT = R1 + R2 + R3

For resistors in

series

I

VT = V1 + V2 + V3

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4Dunblane High SchoolRG

Resistors in Parallel

R1

R3

R2RT

EMF

EMFI

I1

I2

I3I

These two circuits have the

same effective resistance.

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6Dunblane High SchoolRG

Resistors in Parallel

R1

R3

R2RT

VT

EMFI

I1

I2

I3IT

VT/RT = V1/R1 + V2/R2 + V3/R3 BUT

In a parallel circuit

VT = V1 = V2 = V3 (divide by V)

1/RT = 1/R1 + 1/R2 + 1/R3

VT

I = V/R

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