Resistors in Series

RESISTORS IN SERIES

When resistors are connected as in fig 1.12 shows the series combination.

If the resistors are connected end to end the combination is said to be series. The voltage source is connected between the free ends.

Here, there is only one closed loop. Only one current flows (ie) the source current flows through all the elements (ie) current is same through all the resistors but voltage is different. Each resistor has a voltage drop across it is given by ohms law.

V₁ = IR₁, V₂ = IR₂ and V₃ = IR₃

The total drop

V = V₁ + V₂  + V₃

V = IR₁ + IR₂+ IR₃

V = I(R₁ + R₂ + R₃)

R = R₁ + R₂ + R₃

Fig. 1.13 shows the equivalent circuit of fig 1.12. Thus the circuit behaves as if a single resistor R equal to R₁ + R₂ + R₃  is connected across the battery of V volts.

The power dissipated in R₁ is

Similarly

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Total power, P = P₁ + P₂ + P₃

= I²R₁ + I²R₂ + I²R₃

P = I² (R₁ + R₂ + R₃)

In a series circuit:

(i) The same current flows through all the resistances.

(ii) For each resistance, there will be a voltage drop according to ohms law.

(iii) The sum of the voltage drops will be equal to the applied voltage.