Question:

Two equal resistances R$_{1}$ = R$_{2}$= R are connected with a 30 $\Omega$ resistor and a battery of terminal voltage V. The currents in the two branches are 2.25 A and 1.5 A as shown in the figure. Then, what will happen? Please explain the answer in brief.

• A

R$_{2}$= 15$\Omega$

• B

R$_{2}$ = 30$\Omega$

• C

V = 36 V

• D

V = 180 V

Posted by: Srivastava on 07.10.2017

The correct answer is given by option (D).

Explanation: The potential drop across R2 and 30 Ohm will be same as they are in parallel. Now current across R2 is clearly 2.25-1.5 = 0.75 A. Thus,

0.75 x R2 = 30 x 1.5

Therefore, R2 = 60 Ohm = R1.

The equivalent resistance of R2 and 30 Ohm will be

R3 = (60 x 30)/(60 + 30) = 20 Ohm.

Therefore, the total resistance of the circuit is

R4 = R1 + R3 = 80 Ohm

Therefore,

V = 80 x 2.25 = 180 V

Answer A. R2 = 15 Ohm

Total Current is 2.25 A.

The current through the 30 ohm resister is 1.5 A.

Hence Current through the R2 should be equal to 0.75 A (2.25-1.5 = 0.75 A)

If R2 is taken as Unknown, Then  R2 is given by,

By Current didsion method, 1.5  = 2.25 x 30 / (30+R2)

1.5 x (30+R2) = 67.5

45 + 1.5 R2 = 67.5

1.5 R2 = 67.5 - 45

R2 = 22.5 / 1.5

R2 = 15 Ohm

Since, total current in the circuit is constant, we get 2.25R = 0.75R + 1.5*30 .

Or, 1.5R = 1.5*30 .

Hence, R = 30 ohm Ans. (option B)

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