Question

Derive the eqn for equivalent resistance in series and parallel

Answer 1

Derivation of resistance in parallel:

Let us take two resistors with resistance R1 and R2.

We know that current (I) gets divided in parallel.

So let current passing through R1 be I1 and that from R2 be I2.

So I=I1+I2 -------(1)

By ohm's law

I=V/R

So I1=V/R1 and I2=V/R2

Substituting these values in (1)

V/R=V/R1+V/R2

Taking V as common

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

1/R=1/R1+1/R2

Derivation of resistance in series:

Let us take two resistors with resistance R1 and R2.

We know that potential difference(V) gets divided in series.

So let potential difference through R1 be V1 and that through R2 be V2

V=V1+V2 -------(1)

By ohm's law

V=IR

So V1=IR1 and V2=IR2

Substituting these values in (1)

IR=IR1+IR2

Taking I as common

IR=I(R1+R2)

R=R1+R2

Hope you find the answers useful..