If two or more resistors are connected to a battery, the current which will flow through the battery depends on the effective resistance, R_E, of all the resistors. We can consider R_E to be the single resistor which would take the same amount of current from the same battery.

Resistors in Series

In circuit A

Voltage across R₁ is V₁ ....................V₁ = IR₁

similarly, ....................................V₂ = IR_{2 ...........}V₃ = IR₃

Also,........ V₁ + V₂ + V₃ = V

In circuit B

V = IR_E

Combining these two gives

IR_E = IR₁ + IR₂ + IR₃

Resistors in Parallel

In circuit A

Voltage across all the resistors is the same, V.

The current through R₁ is I₁ .............I₁ = V/R₁

similarly, ...............................I₂ = V/R₂ ..............I₃ = V/R₃

Also, ...............I₁ + I ₂ + I ₃ = I

In circuit B

I = V/R_E

Combining these two gives

V/R_E = V/R₁ + V/R₂ + V/R₃