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The rasistance of two conductors in parallel is 12omega and in series is 15ohm. Find the resistance of each conductor.?
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The rasistance of two conductors in parallel is 12omega and in series ...
Let the resistance of 1 resistor is x ohm them of another will be 150-x because in series its 150 similarly put this value on formula on Rp and solve by pair of linear eq surly you will get answer : )
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The rasistance of two conductors in parallel is 12omega and in series ...
Introduction:
The problem states that the resistance of two conductors in parallel is 12 ohms and in series is 15 ohms. We need to find the resistance of each conductor. To solve this problem, we will use the formulas for resistors in parallel and series.

Resistors in Parallel:
When resistors are connected in parallel, the total resistance is given by the formula:

1/R_total = 1/R1 + 1/R2 + 1/R3 + ...

Where R_total is the total resistance and R1, R2, R3, ... are the resistances of the individual conductors.

Resistors in Series:
When resistors are connected in series, the total resistance is simply the sum of the individual resistances:

R_total = R1 + R2 + R3 + ...

Where R_total is the total resistance and R1, R2, R3, ... are the resistances of the individual conductors.

Solution:
Let's assume the resistances of the two conductors are R1 and R2.

Step 1: Find the resistance of the conductors in parallel
Using the formula for resistors in parallel, we have:

1/R_parallel = 1/R1 + 1/R2

Substituting the given resistance of 12 ohms for R_parallel, we get:

1/12 = 1/R1 + 1/R2

Step 2: Find the resistance of the conductors in series
Using the formula for resistors in series, we have:

R_series = R1 + R2

Substituting the given resistance of 15 ohms for R_series, we get:

15 = R1 + R2

Step 3: Solve the equations simultaneously
We now have a system of equations with two unknowns (R1 and R2):

1/12 = 1/R1 + 1/R2
15 = R1 + R2

We can solve this system of equations to find the values of R1 and R2. There are several methods to solve this system, such as substitution or elimination. Let's use the substitution method.

Step 4: Solve the equations using substitution
From the equation 15 = R1 + R2, we can express R1 in terms of R2:

R1 = 15 - R2

Substituting this expression for R1 into the equation 1/12 = 1/R1 + 1/R2, we get:

1/12 = 1/(15 - R2) + 1/R2

Step 5: Simplify the equation and solve for R2
To simplify the equation, we can multiply both sides by 12R2(15 - R2) to eliminate the denominators:

12R2(15 - R2)/12 = 12R2(1/(15 - R2) + 1/R2)

R2(15 - R2) = 12(15 - R2) + 12R2

15R2 - R2^2 = 180 - 12R2 + 12R2

R2^2 - 15R2 + 180 = 0

Step 6:
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The rasistance of two conductors in parallel is 12omega and in series is 15ohm. Find the resistance of each conductor.?
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