Question

A resistor of 10ohm is combined in parallel with another resistor of 'x' ohm. The resultant resistence of the combination is found to be 3.75 ohm. What is the value of 'x'.

Answer 1

Given :

▪ A resistor of resistance 10Ω is connected in parallel with another resistor of resistance xΩ.

▪ The equivalent resistance of the combination is 3.75Ω.

To Find :

▪ The value of x.

Concept :

→ We can calculate the value of x with the help of equivalent resistance formula.

→ Formula of equivalent resistance in parallel connection is given by

☞ 1/Req = 1/R1 + 1/R2

Calculation :

๏ 1/Req = 1/R1 + 1/R2

๏ 1/3.75 = 1/10 + 1/R2

๏ 1/R2 = 1/3.75 - 1/10

๏ 1/R2 = 10-3.75/37.5

๏ R2 = 37.5/6.25

๏ R2 = 6Ω

Answer 2

Given ,

The resistance of 10 ohm and " x " are connected in parrallel and their equivalent resistance is 3.75 ohm

We know that , the equivalent resistance in parrallel combination is given by

$\large \mathtt{ \fbox{\frac{1}{R} = \frac{1}{ R_{1}} + \frac{1}{ R_{2}} + \: .... \: + \frac{1}{ R_{n} } \: \: }}$

Thus ,

➡1/3.75 = 1/10 + 1/x

➡1/x = 1/3.75 - 1/10

➡1/x = (10 - 3.75)/37.5

➡1/x = 6.25/37.5

➡x = 37.5/6.25

➡x = 6 ohm

Hence , the required value of x is 6 ohm