Two 30Ω resistor are connected in series to a source of 200V. When one resistor is connected
across one of them the total circuit resistance is 35Ω. Calculate the power taken by the unknown
resistor.
To calculate the power taken by the unknown resistor, we first need to determine its resistance using the given information.
Let's assume the resistance of the unknown resistor is R.
When two 30Ω resistors are connected in series, their total resistance can be calculated by simply adding them together:
Total resistance = 30Ω + 30Ω = 60Ω
Now, when one resistor is connected across one of them, it means that the unknown resistor (R) and this resistor form a parallel connection. The formula to calculate the total resistance of two resistors in parallel is given by:
1/Total resistance = 1/R + 1/30Ω
Using this formula, we can plug in the value of the total resistance (35Ω) and solve for R:
1/35Ω = 1/R + 1/30Ω
To solve for R, we can use algebraic manipulation:
1/R = 1/35Ω - 1/30Ω
Now, let's find the common denominator and simplify the equation:
1/R = (30 - 35)/(30 * 35Ω)
1/R = -5/(30 * 35Ω)
Multiplying both sides of the equation by R, we get:
1 = -5R/(30 * 35Ω)
Simplifying further, we have:
1 = -R/2100Ω
Multiplying both sides by 2100Ω, we get:
2100Ω = -R
R = -2100Ω
However, resistance cannot have a negative value, so this solution is not valid. Therefore, there might be an error in the problem statement or the given information.
Without the correct value for the unknown resistor, it is not possible to calculate the power taken by it.