Question

Numerical:
A resistance X is connected to a resistance of 15 ohm to get an effective resistance of 6 ohm. Find the value of X . ​

Answer 1

$\huge\bold\underline{ANSWER}}}}}}$

$Let x Ω is connected in parallel to 15Ω to provide an effective resistance of 6Ω$

$\implies$$15x = 6x + 90$

$\implies$$9x = 90$ $\implies$$x = 10$

Answer 2

Given:

We have been given some resistances among which there is a resistance having an unknown value

• Resistance X is connected to a resistance of 15 ohm
• The effective resistance is 6 ohm

Solution:

The given resistance can be connected to 15 ohm resistance in following two ways

• Series Combination
• Parallel Combination

In Series combination , the effective value of resistance comes out to be greater than the given individual resistance

Here , the effective resistance is less than the individual given resistance . Then the combination must be a parallel Combination

Effective Resistance in parallel Combination:

$\large{ \because{ \boxed{ \rm{Eq. \: resistance = \frac{ R_1 \times R_2 }{ R_1 + R_2 } }}}}$

Substituting the values in Equation :

$\longrightarrow \sf{Eq. \: resistance = \dfrac{15x }{15 + x }}$

$\longrightarrow \sf{6 = \dfrac{15x }{15 + x }}$

$\longrightarrow \sf{6 \: ( 15 + x ) = 15x }$

$\longrightarrow \sf{90 + 6x = 15x }$

$\longrightarrow \sf{15x - 6x = 90 }$

$\longrightarrow \sf{9x = 90 }$

$\longrightarrow \sf{x = \dfrac{90}{9} }$

Hence value of x comes out to be :

$\longrightarrow \large{\underline{\boxed{\blue{\rm{x = 10}}}} }$

Hence Value of x is 10 ohm.