Resistance in Series and Parallel

Resistance in Series:

When the resistance of the conductor are joined end to end, they are called Series grouping.

Let R_A, R_B and R_C are connected in Series and V_A,V_B and V_C be the voltage-drops in these corresponding resistance and circuit-current is ‘I’ which is constant in series circuit:

Now, V= V_A+V_A+V_A=IR_A+IR_B+IR_C
V=I(R_A+R_B+R_C)
or, V/I= R_A+R_B+R_C = R = Total or equivalent resistance of the circuit.

Resistance in Parallel:

if the similar ends of each resistance are joined to a common point, and at the other ends, other resistors are joined to another common point then it is said to be a Parallel grouping of resistance.

Let R_A and R_B be the two resistors which are joined in parallel and corresponding current be I_A, I_B and ‘V’ be the voltage applied across each resistor and voltage is constant in parallerl circuit.

Now, circuit ‘I’ = I_A + I_B
Again, I = (V/R_A) + (V/R_B) (applying Ohm’s Law)
=V(1/R_A) + (1/R_B)
or, I/V= (1/R_A) + (1/R_B)=1/R
where R= Total or equivalent resitance of the circuit.