Question

Derive the equivalent resistance when resistors are connected in (i) series (ii) parallel. ( Draw diagram to support your answer) ​

Answer 1

In series connection

When resistors are connected in series the potential difference gets divided

V = V1 + V2....... equation 1

The current through each resistor in series will be the same

According to Ohm's law

V =IR

So,

in our case

V1 = I * R1 ... equation 2

V2= I * R2... equation 3

equation 1 can be weitten as

I*R= V1 + V2

substituting eq 2 and eq3

IR = I * R1 + I * R2

IR = I ( R1 + R2 )

I can be cancelled ( when I in the left side of equation comes to right side it takes the division form and hence gets cancelled)

therefore

R = R1 + R2

In parallel connection

The total current is the sum of the current through all branch circuits in parallel connection

I = I1 + I2

since R is the effective resistance

By ohm's law

V/R = V/R1 + V/R2 ( potential difference through each resistor is same in parallel connection)

V(1/R) = V ( 1/R1 + 1/R2 )

V gets cancelled

so

1/R = 1/R1 + 1/R2

cross multiply,

1/R = (R1 + R2) / R1 * R2

R = (R1 * R2)/R1 + R2

if resistors are of same value then ,

R = r/n

where n is the no.of resistors and r is the resistance of one resistor