A circuit of 4 resistors with a voltage supply of 60 volts,with 3 connected in parallel with 12,18 and 36 ohms are respectively connected in series with the fourth resistor.the power dissipated on the 12 ohm resistor is 36 watts.calculate the resistance of the fourth resistor and the total power in the circuit
Any response to help would be appreciated
To calculate the resistance of the fourth resistor and the total power in the circuit, we can use a combination of Ohm's Law and the power formula.
First, let's calculate the current passing through the circuit. We can use Ohm's Law, which states that V = I * R, where V is the voltage, I is the current, and R is the resistance.
From the given information, we know that the voltage supply is 60 volts and the power dissipated on the 12-ohm resistor is 36 watts. We can use the power formula, P = I^2 * R, to find the current passing through the 12-ohm resistor.
Substituting the given values, we have:
36 watts = I^2 * 12 ohms
Solving for I, we find:
I^2 = 36 watts / 12 ohms
I^2 = 3
I = √3
I ≈ 1.73 amperes
Next, let's analyze the parallel resistors. Since the three resistors are connected in parallel, they have the same voltage across them. The voltage across them is 60 volts, so each of the three resistors receives 60 volts.
To find the current passing through each of the parallel resistors, we can use Ohm's Law again.
For the 18-ohm resistor:
60 volts = I × 18 ohms
I = 60 volts / 18 ohms
I ≈ 3.33 amperes
For the 36-ohm resistor:
60 volts = I × 36 ohms
I = 60 volts / 36 ohms
I ≈ 1.67 amperes
Now, let's find the equivalent resistance of the parallel resistors. In a parallel circuit, the equivalent resistance (R_eq) is calculated using the formula:
1 / R_eq = 1 / R1 + 1 / R2 + 1 / R3
Substituting the values, we have:
1 / R_eq = 1 / 12 ohms + 1 / 18 ohms + 1 / 36 ohms
Simplifying, we find:
1 / R_eq = 1 / 12 ohms + 2 / 36 ohms + 1 / 36 ohms
1 / R_eq = 3 / 36 ohms + 3 / 36 ohms + 1 / 36 ohms
1 / R_eq = 7 / 36 ohms
Taking the reciprocal on both sides, we get:
R_eq = 36 ohms / 7 ≈ 5.14 ohms
Now, we can find the resistance of the fourth resistor. Since the fourth resistor is connected in series with the parallel resistors, the total resistance of the circuit is the sum of the equivalent resistance of the parallel resistors and the resistance of the fourth resistor.
The total resistance (R_total) is given by:
R_total = R_eq + R4
R4 = R_total - R_eq
R4 = Total resistance - Equivalent resistance
R4 = 5.14 ohms
Finally, let's find the total power in the circuit. The power (P) in a circuit is given by the formula:
P = V * I
Since we already have the current (I ≈ 1.73 amperes) and the voltage supply (V = 60 volts), we can find the total power in the circuit:
P = 60 volts * 1.73 amperes
P ≈ 103.8 watts
Therefore, the resistance of the fourth resistor is approximately 5.14 ohms, and the total power in the circuit is approximately 103.8 watts.