Explain the equivalent resistance of a series and parallel resistor network.

Explanation

Resistors in series :
`R_1, R_2, R_3`- Resistors connected in series
V = potential applied
In series, the current flowing throw the resistors is same.
Potential across `R_1, R_2, R_3` are `V_2, V_2, V_3`
repectively.
Total voltage ` V = V_1, V_2, V_3`
According to ohm.s law ` V = IR_1, V_2, IR_2,`
`V = IR_3, V= IR_s`
`V = IR_1 + IR_2 +IR_3`
`IR_s = I (R_1 + R_2 +R_3)`
(Equivalent restance ) `R_s = R_1 + R_2 R_3`

(a) three resstors in series

The equivalent resistance of a series is the sum of the individual resistances.
`R_s` is always greater then each individual resistance.
Resistor in parallel :
`R_1, R_2, R_3,` -Resistances connected in parallel
V - Applied voltage.
In parallel the voltage across each rasistor is same.
Current in resistor `R_2, R_2` and `R_3` are `I_1, I_2, I_3` respectively,
According to Ohm.s law :
`I_1 = V/R_1 , I_2 = V/R_2 ,I_3`
`V/R_3 , I = V/R_P`
`V/R_p = V/R_1 + V/R_2 + V/R_3 rArr V/R_p = V(1/R_1 + 1/R_2+1/R_3)`
`1/R_p = 1/R_1 + 1/R_2 + 1/R_3`
`R_p` equivalent resistance of the parallel combination of resistors. The sum of the reciprocal of effective resistance.
`R_p` is lesser than each individual, resistance.