Ignoring any effects of dc resistance, what is the total reactance of a 250 mH coil in series with a 4.7 microfarad capacitor at a signal frequency of 1000 Hz?

To find the total reactance of a coil (inductor) in series with a capacitor, we first need to calculate the individual reactances of the coil and the capacitor, and then subtract the capacitive reactance from the inductive reactance.

1. Calculate the inductive reactance (X_L) using the formula: X_L = 2πfL Where: f = frequency = 1000 Hz L = inductance = 250 mH = 0.25 H X_L = 2π * 1000 Hz * 0.25 H = 1570.8 ohms

2. Calculate the capacitive reactance (X_C) using the formula: X_C = 1 / (2πfC) Where: C = capacitance = 4.7 µF = 4.7 * 10^-6 F X_C = 1 / (2π * 1000 Hz * 4.7 * 10^-6 F) = 33.86 ohms

3. The total reactance (X_T) of the coil and capacitor in series is given by: X_T = X_L - X_C X_T = 1570.8 ohms - 33.86 ohms = 1536.94 ohms

So, the total reactance of a 250 mH coil in series with a 4.7 microfarad capacitor at a signal frequency of 1000 Hz is approximately 1537 ohms.