Question

You have a resistor 200 ohm, a 0.400-H inductor, a 5.00 uF capacitor, and a variable frequency ac source with an amplitude of 3.00 V. You connect all four elements together to form a series circuit. What will be the current amplitude at an angular frequency of 400rad/s? At this frequency, will the source voltage lead or lag the current?

Answer 1

To find the current amplitude at an angular frequency of 400 rad/s, we need to calculate the impedance and use Ohm's Law. The source voltage will lead or lag the current depending on the phase angle.

Step-by-step explanation:

Using the given values, we can calculate the impedance (Z) of the series circuit. The impedance is given by:

Z = sqrt((R^2) + ((ωL - 1/(ωC))^2))

Where R is the resistance, L is the inductance, C is the capacitance, and ω is the angular frequency.

At an angular frequency of 400 rad/s, we can substitute the values and calculate Z. Once we have Z, we can use Ohm's Law to calculate the current amplitude (I). Ohm's Law states that I = V/Z, where V is the source voltage.

The source voltage will lead the current if the phase angle is positive, and it will lag the current if the phase angle is negative. We can calculate the phase angle using the expression:θ = atan((ωL - 1/(ωC)) / R)