Everything Science Grade 11

CHAPTER 19. ELECTRIC CIRCUITS 19.3

We know that in a series circuit the current hasto be the same in all components. So we can write:

I = I 1 = I 2 = I 3

We also know that totalvoltage of the circuit hasto be equal to the sum of the voltages over all three
resistors. So we can write:

V = V 1 + V 2 + V 3

Finally, we know that Ohm’s Law has to apply for each resistor individually, which gives us:

V 1 = I 1 · R 1

V 2 = I 2 · R 2

V 3 = I 3 · R 3

Therefore:

V = I 1 · R 1 + I 2 · R 2 + I 3 · R 3

However, because

I = I 1 = I 2 = I 3

, we can further simplifythis to:

V = I· R 1 + I· R 2 + I· R 3

= I(R 1 + R 2 + R 3 )

Further, we can write anOhm’s Law relation forthe entire circuit:

V = I· R

Therefore:

V = I(R 1 + R 2 + R 3 )

I· R = I(R 1 + R 2 + R 3 )

∴ R = R 1 + R 2 + R 3

DEFINITION: Equivalent resistance ina series circuit,Rs

For n resistors in series the equivalent resistance is:

Rs= R 1 + R 2 + R 3 +··· + Rn

See simulation: VPmgvat http://www.everythingscience.co.za)

Let us apply this to the following circuit.