Question

Derive the formula of equivalent resistance for series connection of resistances.​

Answer 1

According to Ohm's law, the voltage drop, V, across a resistor when a current flows through it is calculated by using theequation V=IR, where I is current in amps (A) and R is the resistance in ohms (Ω). This implies that the total resistance in aseries is equal to the sum of the individual resistances.

Answer 2

EXPLANATION.

Formula of equivalent resistance for series connection of resistance.

As we know that,

In series combination, same current  through the resistor but voltage is different in different resistors.

Let current (I)  through the resistor.

If V is the voltage and V₁, V₂, V₃  through each resistors R₁, R₂, R₃.

According to the ohm's law, we get.

⇒ V = IR.

⇒ V₁ = IR₁.

⇒ V₂ = IR₂.

⇒ V₃ = IR₃.

⇒ V = V₁ + V₂ + V₃.

⇒ IR(S) = IR₁ + IR₂ + IR₃.

⇒ R(S) = R₁ + R₂ + R₃