Two resistors 15ohm and B ohm are connected in parallel.This combination is connected in series to a 5ohm resistor and a battery of 5 volt.If current passing through B resistor is 1/3A,find B?

Question

Answer

Problem:

Two resistors 15ohm and B ohm are connected in parallel. This combination is connected in series to a 5ohm resistor and a battery of 5 volt. If current passing through B resistor is 1/3A, find B?

Solution:

Step 1: Calculate the equivalent resistance of parallel combination

When two resistors are connected in parallel, the equivalent resistance can be calculated using the formula:

1/Req = 1/R1 + 1/R2

where Req is the equivalent resistance, R1 and R2 are the resistances of the two resistors

Substituting values, we get:

1/Req = 1/15 + 1/B

Multiplying both sides by 15B, we get:

15B/15B + 15 = B/15B + B

Simplifying, we get:

Req = 15B/(15 + B)

Step 2: Calculate the total resistance

When resistors are connected in series, the total resistance can be calculated by adding the individual resistances of the resistors. Therefore, the total resistance of the circuit is:

Rt = Req + 5

Substituting the value of Req, we get:

Rt = 15B/(15 + B) + 5

Step 3: Calculate the current passing through the circuit

Using Ohm's law, the current passing through the circuit can be calculated by dividing the voltage by the total resistance. Therefore, the current passing through the circuit is:

I = V/Rt

Substituting the values of V and Rt, we get:

I = 5/(15B/(15 + B) + 5)

Step 4: Calculate the value of B

We are given that the current passing through the B resistor is 1/3A. Therefore, we can equate the current passing through the circuit to the sum of the currents passing through the two resistors in parallel. Therefore, we get:

I = IB + I15

Substituting the values of I and IB, we get:

5/(15B/(15 + B) + 5) = 1/3 + 5/(15 + B)

Multiplying both sides by (15 + B), we get:

5(15 + B)/(15B + 75 + 5(15 + B)) = 1/3 + 5/(15 + B)

Simplifying, we get a quadratic equation:

2B^2 - 95B + 225 = 0

Solving the equation, we get:

B = 15 or B =

Answer

2.5

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