Question

solution required ??????? ​

Answer 1

$\bigstar$ Given:-

Parallel combination of 8 Ohm and 12 Ohm resistors

$\bigstar$ To Find:-

Effective resistance of the parallel combination

$\bigstar$ Solution:-

We know that

In parallel combination of resistance, resistors are connected at same point. Current through the resistor is different and voltage through the resistor is same.

Parallel Resistor Equation

$\red{\rm \longrightarrow \dfrac{1}{R_{p}}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+.......+\dfrac{1}{R_{n}}}$

As only two resistors are given here

We get;

$\pink{\rm \longrightarrow \dfrac{1}{R_{p}}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}$

Hence;

$\orange{\rm \longrightarrow R_{p}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}}}$

Here;

$\rm R_{p}$ = effective resistance in parallel

$\rm R_{1}$ = given resistance in question

$\rm R_{2}$ = given resistance in question

Units

Resistance = Ohm (Ω)

According to the question:-

We are asked to find the effective resistance of the parallel combination

Therefore;

We must find $\rm "R_{p}"$

Given that

Parallel combination of 8 Ohm and 12 Ohm resistors

Hence;

$\rm R_{1}=8 \ \Omega$

$\rm R_{1}=12 \ \Omega$

Substituting the values

We get;

$\blue{\rm \longrightarrow R_{p}=\dfrac{8 \times 12}{8+12} \ \Omega}$

$\green{\rm \longrightarrow R_{p}=\dfrac{96}{20} \ \Omega}$

On further simplification

We get

$\purple{\rm \longrightarrow R_{p}=4.8 \ \Omega}$

Therefore

Effective resistance = 4.8 Ω

Hence

$\checkmark$ Option (3) is correct