Question

Write expression of the combination of resistances ​

Answer 1

Two resistors of resistance R1 and R2 are connected in series. Let I be the current through the circuit. The current through each resistor is also I. The two resistors joined in series is replaced by an equivalent single resistor of resistance R such that the potential difference V across it, and the current I through the circuit remains same.

As , V = IR , V1 = IR1 , V2 = IR2

IR = IR1 + IR2

IR = I (R1 + R2)

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Answer 2

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•Derivation of mathematical expression of resistances in series combination

• : Let R1, R2 and R3 be the resistances connected in series

, I be the current flowing through the circuit, i.e., passing through each resistance, and V1, V2 and V3 be the potential difference across R1, R2 and R3, respectively. Then, from Ohm’s law,

V1 = IR1, V2 = IR2 and V3 = IR3 ...(ii)

If, V is the potential difference across the combination of resistances then,

V = V1 + V2 + V3 ...(iii)

If, R is the equivalent resistance of the circuit, then V = IR ...(iv)

Using Eqs. (i) to (iv) we can write,

IR = V = V1 + V2 + V3

= IR1 + IR2 + IR3

IR = I (R1 + R2 + R3)

R = R1 + R2 + R3

Therefore, when resistances are combined in series, the equivalent resistance is higher than each individual resistance.

Some results about series combination :

(i) When two or more resistors are connected in series, the total resistance of the combination is equal to the sum of all the individual resistances.

(ii) When two or more resistors are connected in series, the same current flows through each resistor.

(iii)When a number of resistors are connected in series, the voltage across the combination (i.e. voltage of the battery in the circuit), is equal to the sum of the voltage drop (or potential difference) across each individual resistor.