Resistors in Series and Parallel

The total resistance of resistors placed in series is the sum of the individual resistances.The potential differences across all the resistors will be the sum of the potential differences across each resistor but the current will be the same through each resistor.Given V_total = V₁ + V₂and V = IR from the definition of resistanceIR_total = IR₁ + IR₂so R_total = R₁ + R₂
In parallel the currents add up to the total current soI_total= I₁ + I₂Given

I

=

V R

from the definition of resistanceand the potential difference V is the same

V Rtotal

=

V R1

+

V R2

so

1 Rtotal

=

1 R1

+

1 R2