Question

Explain and derive equivalent Resistance formula for 3 Resistors connected in Pure Series. Generalize the formula?

Answer 1

When three resistors are connected in series, then the same current passes through each resistor but the voltage drop is different for each resistor.

We know that applied voltage is$\left(V\right)$

$\therefore V=V_1+V_2+V3$

we also know that,

$V=I\cdot R$ (from ohm's law)

$\therefore I\cdot R_{eq}=I\cdot R_1+I\cdot R_2+I\cdot R_3$

$\Rightarrow I\cdot R_{eq}=I\cdot (R_1{+R}_2+R_3)$

$\Rightarrow$ $R_{eq}=R_1{+R}_2+R_3$

It can be extended for $n$ resistors

$R_{eq}=$ $R_1+R_2....................................R_n$

So, the equivalent resistance or the total resistance of the circuit can be defined as a single value of resistance that can replace any number of resistors connected in series without altering the vlaues of the current or the voltage in the circuit.