In a circuit with 25 ohms resistance and 50 ohms capacitive reactance, what is the calculated impedance?

In a circuit with 25 ohms resistance and 50 ohms capacitive reactance, what is the calculated impedance?

• A. 40.50
• B. 50.90
• C. 55.90
• D. 60.10

Answer: (C)

To determine the impedance in a circuit that includes both resistance and capacitive reactance, it's essential to use the formula for the impedance of an R-C circuit. The impedance \( Z \) can be calculated using the formula: \[ Z = \sqrt{R^2 + X_C^2} \] where \( R \) is the resistance, and \( X_C \) is the capacitive reactance. In this case, the resistance \( R \) is 25 ohms, and the capacitive reactance \( X_C \) is 50 ohms. Plugging these values into the formula gives: 1. Calculate \( R^2 \): \[ R^2 = 25^2 = 625 \] 2. Calculate \( X_C^2 \): \[ X_C^2 = 50^2 = 2500 \] 3. Add the squared values: \[ R^2 + X_C^2 = 625 + 2500 = 3125 \] 4. Take the square root to find \( Z \): \[ Z = \sqrt{3125} \approx 55.90

To determine the impedance in a circuit that includes both resistance and capacitive reactance, it's essential to use the formula for the impedance of an R-C circuit. The impedance ( Z ) can be calculated using the formula:

[

Z = \sqrt{R^2 + X_C^2}

]

where ( R ) is the resistance, and ( X_C ) is the capacitive reactance.

In this case, the resistance ( R ) is 25 ohms, and the capacitive reactance ( X_C ) is 50 ohms. Plugging these values into the formula gives:

1. Calculate ( R^2 ):

[

R^2 = 25^2 = 625

]

2. Calculate ( X_C^2 ):

[

X_C^2 = 50^2 = 2500

]

3. Add the squared values:

[

R^2 + X_C^2 = 625 + 2500 = 3125

]

4. Take the square root to find ( Z ):

[

Z = \sqrt{3125} \approx 55.90