Explanation:

Resistance R

net

=

R

1

1

+

R

2

1

1

=

R

1

+R

2

R

1

R

2

which is less than R

1

and R

2

. As

R

1

−R

net

=R

1

−

R

1

+R

2

R

1

R

2

=

R

1

+R

2

R

1

2

>0⇒R

1

−R

net

>0⇒R

1

>R

net

R

2

−R

net

=R

2

−

R

1

+R

2

R

1

R

2

=

R

1

+R

2

R

2

2

>0⇒R

2

−R

net

>0⇒R

2

>R

net

Answer:

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12th

Physics

Current Electricity

Problems on Combination of Resistors

(a) With the help of a diag...

PHYSICS

(a) With the help of a diagram , derive the formula for the resultant resistance of three resistors connected in series.

(b) For the circuit shown in the diagram given below :

Calculate :

(i) the value of current through each resistor.

(ii) the total current in the circuit.

(iii) the total effective resistance of the circuit.

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ANSWER

(a)

Fig shows three resistances R

1

,R

2

and R

3

connected in series with a battery of V volts.

Let the p.d. across R

1

,R

2

and R

3

is V

1

,V

2

and V

3

respectively.

s.t.V=V

1

+V

3

+V

2

--------------(1)

Let the equivalent resistance be R and the current flowing through the whole circuit is I.

By ohm's law,

I

V

=R

V=I×R------------------(2)

Applying ohm's law to both R

1

,R

2

and R

3

.

V=I×R

1

------------------(3)

V=I×R

2

------------------(4)

V=I×R

3

------------------(5)

From eqs. (1) , (2) , (3) , (4) and (5) , we get

I×R=I×R

1

+I×R

2

+I×R

3

I×R=I×(R

1

+R

2

+R

3

)

R=R

1

+R

2

+R

3

in parallel

In this combination the main current I divide in three part I1, I2 and I3 at the junction point that is different amount of current flowing through the registers but the potential difference across them be same as V volt.

It is clear from the circuit:

Total current at junction point:

I = I1 + I2 + I3 -------(1)

By ohm's law

V = RI

Hence, I = V/R

Thus,

current in 1st resistor, I1 = V/R1

current in 2nd resistor, I2 = V/R2

current in 3rd resistor, I3 = V/R3

If the equivalent resistance of this combination be “R”omh, then current flowing in equivalent resistance:

I = V/R

All these values put in eqn1

V/R = V/R1 + V/R2 + V/R3

V/R = V (1/R1 + 1/R2 + 1/R3)

[ 1/R = 1/R1 + 1/R2 + 1/R3 ]