Question

derive the equation for resultant resistance of resistors in series ​

Answer 1

When resistors are in series, then the total voltage of the system is the sum of the individual voltages.

Let us consider 3 resistors of resistances R1, R2 and R3 ohms, and of voltages V1, V2 and V3 volts. The current across each resistor is I amperes as they're in series.

Let the effective voltage be V volts and the effective resistance be R ohms.

Remember the Ohm's law, V = IR.

As per the first statement here, the mathematical equation is as follows...

V = V1 + V2 + V3

I (V) = I (V1 + V2 + V3)

IV = IV1 + IV2 + IV3

R = R1 + R2 + R3 <Ohm's law>

THUS, THE RESULTANT OR EFFECTIVE RESISTANCE OF RESISTORS IN SERIES IS THE SUM OF THE RESISTANCE OF THE INDIVIDUAL RESISTORS.

ALSO, THE EFFECTIVE RESISTANCE OF THE RESISTORS IN SERIES IS ALWAYS GREATER THAN THE RESISTANCE OF THE INDIVIDUAL RESISTORS.

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