Question

to create a voltage drop consisting of just the dc voltage of a signal across a resistor, you must bypass the ac voltage using a(n) _____ connected in parallel.

• capacitor with a reactance of 10 times the resistor’s value
• capacitor with a reactance of one - tenth the resistor’s value
• inductor with a reactance of 10 times the resistor’s value
• inductor with a reactance of one - tenth the resistor’s value

Explanation:

To bypass AC voltage and have only DC voltage across a resistor, we use a capacitor in parallel. The reactance of the capacitor (\(X_C = \frac{1}{2\pi f C}\)) should be much smaller than the resistor's resistance for effective AC bypass. A capacitor with reactance of one - tenth the resistor’s value (\(X_C=\frac{R}{10}\)) means it offers low impedance to AC, allowing AC to pass through the capacitor (bypassing the resistor for AC), while DC (which capacitor blocks) goes through the resistor. If reactance is 10 times the resistor's value, it's high impedance for AC, not good for bypassing. Inductors block DC and pass AC, so they can't be used here as we need to keep DC across the resistor.

Answer:

capacitor with a reactance of one - tenth the resistor’s value