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

Answer

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Hint: When three resistors are concealed in derives then the same current passes through each resistor but the voltage drop is different for each resistor.

Complete step by step solution:
According to Ohm’s formula V = IR.
When three resistors are connected in series then the same current passes through each resistor but the voltage drop is different for each resistor. If V is the applied voltage and

V_{1}, V_{2}

and

V_{3}

is voltage across resistance

R_{1}, R_{2} a n d R_{3}

respectively then.

V = V_{1} + V_{2} + V_{3}

…(1)

According to ohm’s law
V = IR

∴

I R_{e q} = I R_{1} + I R_{2} + I R_{3}

I R_{e q} = I (R_{1} + R_{2} + R_{3})

R_{e q} = R_{1} + R_{2} + R_{3}

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 value of the current or the voltage of the circuit.
If we have n resistance connected in series, then generalized formula for equivalent resistance is

R_{e q} = R_{1} + R_{2} + R_{3} . . . . . . . + R_{n}

We know that applied voltage is (v)

∴ V = V_{1} + V_{2} + V_{3}

We also know that
V = IR (from ohm’s law)

∴ I R_{e q} = I R_{1} + I R_{2} + I R_{1}

\Rightarrow I R_{e q} = I (R_{1} + R_{2} + R_{3})

\Rightarrow R_{1} + R_{2} + R_{3}

So, the equivalent resistance or the total resistance of the circuit can be defined as a single value of resistor connected in series with altering the values of the current or voltage in the circuit.

Note: If three or more resistors with the same value are connected in parallel, then the equivalent resistance is equal to