Question

derive an expression for resistors connected in parallel combination​

Answer 1

Answer:

Let us make a circuit as shown in following diagram. Let us assume that three resistors R

1

,R

2

and R

3

are in parallel combination. Currents I

1

,I

2

and I

3

are flowing respectively through R

1

,R

2

and R

3

. Potential difference in the circuit is V and current through the circuit is I.

As per Ohm's Law:

Current through R

1

is I

1

=

R

1

V

Current through R

2

is I

2

=

R

2

V

Current through R

3

is I

3

=

R

3

V

And current through the circuit is I=

R

V

where R is equivalent resistance

Using above equations, we get

I=I

1

+I

2

+I

3

or, I=

R

1

V

+

R

2

V

+

R

3

V

or, I=v(

R

1

1

+

R

2

1

+

R

3

1

)

this means that;

R

1

=

R

1

1

+

R

2

1

+

R

3

1