Question

Two resistors are in the ratio 1:4. If these are connected in parallel there total resistance becomes 20 ohm. Find the value of each resistance.

Answer 1

Answer:

let the resistance be 1x and 4x

answer is 25 ohm and 100 ohm

Explanation:

1/R = 1/R1 +1/R2

1/20= 1/x +1/4x

1/20 = 5x/4x²

1/20 = 5/4x

4x/5= 20

x= 100/4

x = 25

so the two resistors

x and 4x

25 ohm and 100 ohm

Answer 2

Answer:

The 1st Resistor, R1 = x = 25 Ω

The 2nd Resistor, R2 = 4x = 4 × 25 = 100 Ω

Explanation:

Given,

Two resistors are in the ratio = 1:4

Let the first resistors be x.

Let the second resistors be 4x.

By using the formula of parallel combination of resistors.

1/Rp =1/R1 + 1/R2

.°. Rp = R1 × R2 / R1 + R2

Putting the values

=> 20 = x × 4x / x + 4x

=> 20 = 4x² / 5x

=> 20 = 4x × x / 5 × x

'x' is canceled.

=> 20 = 4x / 5

=> 20 × 5 = 4x

=> 100 = 4x

=> 4x = 100

=> x = 100 / 4

.°. x = 25

Now, putting the values of x to get the resistance of resistors.

So,

The 1st Resistor, R1 = x = 25 Ω

The 2nd Resistor, R2 = 4x = 4 × 25 = 100 Ω