Question

What resistance must be Connected
in parallel to 4 ohm resistance to make the effective resistance equal to 2.4 ohms.​

Answer 1

From the question we have,

• We need to find the resistance to be connect to a 4 ohm resistance in order to make the effwctive resistance 2.4 ohm.

Let the resistance to be connected be x,

We know that, effective resistance when resistors are in parallel;

= $\sf{Resistance_{eff.}}$ = $\sf{\dfrac{1}{R1} + \dfrac{1}{R2} + .... \dfrac{1}{Rn}}$

So, put the values in the formula:

= $\sf{Resistance_{eff.}}$ = $\sf{\dfrac{1}{R1} + \dfrac{1}{R2}}$

= 2.4 = $\sf{\dfrac{1}{4} + \dfrac{1}{x}}$

= 2.4 = $\sf{\dfrac{x + 4}{4x} }$

= 2.4(4x) = x + 4

= 9.6x = 4

= 9.6x - x = 4

= 8.6 x = 4

= x = $\sf{\dfrac{4}{8.6} }$

= x = $\sf{\dfrac{40}{86} }$

= x = 0.46

Therefore, the resistor we need to connect is of 0.46 ohm.