Question

drive the expression for resistance in series combination​

Answer 1

Answer:

The resistors are connected across two points in the circuit in such a way that the current flowing through each resistor is the same and only one path is available for it to flow, then the resistors are said be connected in series.

In the figure above, three resistors R

1

,R

2

and R

3

are connected in series across the points A and B. Hence, the current (I) flowing through each of the resistors is same but the total voltage of the battery gets divided.

If the voltage drops across V

1

,V

2

and V

3

are R

1

,R

2

and R

3

respectively then,

V=V

1

+V

2

+V

3

.(i)

Now, if the resistor R instead of these three resistances R

1

,R

2

and R

3

is connected in such a way that the current flowing through the circuit remains the same, then R is called the equivalent resistance of the circuit.For an equivalent resistor, V = IR.(ii)

According to Ohms law,

R

1

voltage drops across, V

1

=IR

1

..(iii)

R

2

voltage drops across, V

2

=IR

2

..(iv)

R3 voltage drops across, V

3

=IR

3

..(v)

Adding (iii), (iv) and (v):

V

1

+V

2

+V

3

=IR

1

+IR

2

+IR

3

(vi)

Or, V=IR=I(R

1

+R

2

+R

3

)

Or, R=R

1

+R

2

+R

3

Thus, in a series connection, the equivalent resistor R is equal to the sum of all the resistors connected in the series.

solution

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Answer 2

Laws of resistances in series: (i) Current through each resistance is same. (ii) Total voltage across the combination = Sum of the voltage drops. (iii) Voltage drop across any resistor is proportional to its resistance.

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