Question

Write formulas of equivalent resistance if

(a) Resistance are in parallel

(b) Resistance are in series​

Answer 1

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In series combination, resister are connected end to end and current has a single path through the circuit but the potential difference varies across each resistor. Thus we can write as,

V = V1 + V2 + V3

according to Ohm's law V = IR So,  

V1 = I R1, V2 = I R2, V3 = I R3

V = I R1 + I R2 + I R3

V = I(R1+R2+R3)

V =IRe

All the individual resistances become equal to the equivalent resistance.

or Re = R1 + R2 + R3......Rn

In parallel combination, each resistor'sone is connected to the positive terminal while the other end is connected to a negative terminal. The potential difference across each resistance is the same and the current passing through them is different.

V = V1 =V2=V3

I  = I1+ I2+I3

Current throught each resistor will be:

I1= V/R1 , I2 = V/R2 = I3 = V/R3

I = V (1/R1+ 1/R2+1/R3)  

In case of equivalent resistance I=V/Re

V/Re =  V (1/R1+ 1/R2+1/R3)

So the equivalnet resistance is the sum of all resistances

   1/Re = 1/R1+ 1/R2+1/R3