Question

Four resistors having resistance values 4 ohm, 8 ohm, 12 ohm and 24 ohm are connected in parallel. Find the equivalent resistance of the combination.​

Answer 1

Explanation:

ANSWER:-

We know that:-

• For parallel resistance, It will be the reciprocal of the given value.

So, according to given value,

Let us Assume the value as $R_p$

Now,

$\dfrac{1}{4}+\dfrac{1}{8}+\dfrac{1}{12}+\dfrac{1}{24}$=$\dfrac{1}{R_p}$

Now,

LCM of 4,8,12 and 24 gives 24.

$\dfrac{1}{R_p}$= $\dfrac{6+3+2+1}{24}$

$\dfrac{1}{R_p}$=$\dfrac{12}{24}$

$\dfrac{1}{R_p}$=$\dfrac{1}{2}$

$\boxed{\sf{R_p = 2 \Omega }}$

So, the Equivalent Resistance is 2 ohm.

Things to Note:-

• The Parallel combination is a most suitable combination as it allows all the appliances to work independently.
• Series combination are those which are added simply.
• While in series combination, the appliances are inter dependent. If one appliances gets damaged, it affects the whole circuit.
• The equivalent resistance of Parallel combination is less than what is given.
• The equivalent resistance of Series combination is more than what is given.