Question

What is the value of unknown resistance to be connected in parallel to a 75 kΩ to reduce the total resistance to 10 kΩ?

Answer 1

Step-by-step explanation:

$let \: it \: be \: r \\ \\ then \: \: \: \frac{75r}{75 + r} = 10 \\ \\ 75r = 750 + 10r \\ \\ 65r = 750 \\ \\ r = \frac{750}{65} = \frac{150}{13} k \: \: ohms$

Answer 2

The value of unknown resistance to be connected in parallel is 11.5kΩ.

Given:-

Resistance in parallel = 75kΩ

Total resistance = 10kΩ

To Find:-

The value of unknown resistance to be connected in parallel.

Solution:-

We can easily find out the value of unknown resistance to be connected in parallel by using these simple steps.

As

Resistance in parallel (r1) = 75kΩ

Total resistance (r) = 10kΩ

Unknown resistance (r2) =?

Here, all the resistance are in Resistance in kilo ohm, so we don't need to change them. and the final answer will also come in kilo ohm.

According to the formula of of equivalent resistance in parallel,

$\frac{1}{r} = \frac{1}{r1} + \frac{1}{r2}$

on taking LCM,

$\frac{1}{r} = \frac{r1 + r2}{r1 \times r2}$

$r = \frac{r1 \times r2}{r1 + r2}$

on putting the values of r1 and r in the above equation we get,

$10 = \frac{75 \times r2}{75 + r2}$

$10(75 + r2) = 75 \times r2$

$75 \times 10 + 10 \times r2 = 75r2$

$750 + 10r2 = 75r2$

$750 = 75r2 - 10r2$

$750 = 65r2$

$r2 = \frac{750}{65}$

$r2 = 11.5kΩ$

Hence, The value of unknown resistance to be connected in parallel is 11.5kΩ.

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