Question

what is total resistance in series and in parallel when 2 resistance taken R1 and R2 class 10​

Answer 1

When resistors are in series;

• The Current would be same

• But, the Voltage is different.

So, let's consider voltage.

V = V₁ + V₂

By Ohm's law,

V = IR₁ + IR₂

⇒ V = I(R₁ + R₂)

⇒ V ÷ I = R₁ + R₂

⇒ R = R₁ + R₂

When resistors are in parallel;

• Voltage would be same
• Current would be different.

So, let's consider current in the circuit

I = I₁ + I₂

By Ohm's law,

I₁ = V ÷ R₁

I₂ = V ÷ R₂

Substituting these values,

I = I₁ + I₂

$\implies \sf{\dfrac{V}{R} = \dfrac{V}{R_{1}}+ \dfrac{V}{R_{2}}}$

$\implies \sf{\dfrac{V}{R}= V\bigg(\dfrac{1}{R_{1}}+ \dfrac{1}{R_{2}}\bigg)}$

$\implies \boxed{\bf{\dfrac{1}{R}= \dfrac{1}{R_{1}}+ \dfrac{1}{R_{2}}}}$