Resistances in series

When some resistors are connected such as first resistor’s ending point connects to second resistor’s first point and second resistor’s last point connects to third resistors first point thus some resistors are connected and same current I flows through each resistor. Then we can say the combination is series combination of series resistance.

We consider given figure shown where resistance in a series circuit.

Here R₁ and R₂ are connected at B point and R₂ and R₃ resistor are connected at C point for resistance series circuit. A is first point of R₁ resistor and D is ending point of R₃ resistor.

Equivalent series resistance:

Consider Voltages of A, B, C and D points are V_A, V_B, V_C and V_D. Where V_A > V_B

Consider, same current I flows through each resistor. Now applying Ohm’s law different parts in the circuit.

We get,

Between A and B point, V_A – V_B = IR₁

Between B and C point, V_B – V_C = IR₂

Between C and D point, V_C – V_D = IR₃

Adding A to D point,

V_A – V_D = I (R₁ + R₂ + R₃ )—————– (i)

If we replace R_1, R₂, and R₃ resistance by R_S as equivalent resistance.

Let, current I flows across the circuit. Then we will get same voltage between A and D point, So R_S is the equivalent resistance of series resistance.

Applying Ohm’s law for resistors series,

V_A – V_D = IR_S ———————- (ii)

From equation (i) & (ii),

IR_S = I (R₁ + R₂ + R₃)

Or, R_S =  R₁ + R₂ + R₃ + ———————–+ R_n

This is the equation of resistance in series circuit.

It means sum of all resistance is the equivalent resistance for series combination of resistance.