Question

if the total resistance of the given circuit is 20 ohm then calculate the resistance of X and current​

Answer 1

Let .

r1 = 10 ohm

r2 = x

r3 = 25

r4 = 75

r1 and r2 in series ...

so,. r5 = r1 +r2.

r5 = 10+x

r3 and r4 are in series ...

.

so , r3 + r4 = 25 +75

....r6 = 100

now , r5 and r6 in parallel

so 1/ 10+x + 1/100 = 20

. 1/10+x = 20- 1/100

.... 1/10+x = 100

1 = 1000 + 100x

.... x = 10 ohm

Answer 2

Answer:

X = 15 ohm

I is 0.6 amp

Explanation:

Total resistance, 20 Ohm = [1/(10 + X) + 1/(25 + 75)]⁻¹

Because, 10 ohm and X ohm resistances are in series; 25 ohm and 75 ohm resistances are in series.

The effective resistances (10 + X) ohm and (25 + 75) ohm are in parallel.

So,

$20 = \left[ \dfrac{1}{10 + X} + \dfrac{1}{100} \right] ^ {-1}\\\\\\\implies \dfrac{1}{20} = \dfrac{100 + 10 + X}{(10+X)100}\\\\\\\implies \dfrac{1}{20} = \dfrac{110 + X}{1000 + 100X}\\\\\\\implies 1000 + 100X = 20(110 +X)\\\\\\\implies 1000 + 100X = 2200 + 20X\\\\\\\implies 100X - 20X = 2200 -1000\\\\\\\implies 80X = 1200\\\\\\\implies X = 15 \Ohm$

V = 6 v

R = 15 ohm

So, I = v/r = 6/15 = 3/5 = 6/10 = 0.6 amp