Combination of Resistors - Series combination of resistor

SERIES COMBINATION OF RESISTORS

In series combination of resistors, resistances are connected in such a way that they form a single electrical path. Thus same elctric current flows through all resistors. And depending upon the value of resistors, the voltage gets divided among them. i.e voltage drop across each resistance is different.

Let R₁, R₂ and R₃ be the resistors connected in series as shown in the figure. And the voltage drop across each resistance be V₁, V₂ and V₃.

According to Ohm’s law

V=IR        ------------------------- (1)

The total voltage is given by

V = V₁+V₂+V₃

Now, V₁ = IR₁

V₂ = IR₂

V₃ = IR₃

Therefore, equation (1) becomes

IR = IR₁ + IR₂ + IR₃

IR = I (R₁ + R₂ + R₃)

R = R₁ + R₂ + R₃

Thus we can say that in series combination of resistors the equivalent resistance of the circuit increases.

NOTE: Case 1: If all resistors connected in circuit are of same value i.e

R1 = R2 = R3 = R

R = R + R + R

R = 3R

Hence if ‘n’ number of resistances connected in series then

R _series = n R

And the potential difference across each resistance is given by

V’ = V/n

Key Points:

1. Current remains constant
2. Voltage is divided among the resistors
3. Equivalent resistance of the circuit increases

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