Two 250-µF capacitors, with equal capacitances, and a 1.5-mH inductor are connected as shown in the figure. It is desired to "drive" the circuit by placing an ac generator in series with the inductor. Which output voltage for the generator will produce the largest current in the above circuit? Assume that V is in volts when t is in seconds.

Question

Two 250-µF capacitors, with equal capacitances, and a 1.5-mH inductor are connected as shown in the figure. It is desired to "drive" the circuit by placing an ac generator in series with the inductor. Which output voltage for the generator will produce the largest current in the above circuit? Assume that V is in volts when t is in seconds.

Answer 1

is unfortunately "as shown in figure" somewhere

Answer 2

To determine the output voltage for the generator that will produce the largest current in the circuit, we need to analyze the circuit configuration shown in the figure.

Unfortunately, there is no figure provided in your question, so I won't be able to refer to it directly. However, I can guide you through the necessary steps to find the answer.

Let's assume that the ac generator provides a sinusoidal voltage waveform of the form V(t) = Vm * sin(ωt), where Vm represents the peak voltage and ω is the angular frequency.

To find the output voltage that maximizes the current in the circuit, we need to consider the concept of resonance. In a series RLC circuit like this, resonance occurs when the inductive reactance (XL) equals the capacitive reactance (XC).

The reactance of an inductor is given by XL = ωL, where L is the inductance in henries, and the reactance of a capacitor is given by XC = 1 / (ωC), where C is the capacitance in farads.

At resonance, XL = XC. Therefore, we can equate the two expressions:

ωL = 1 / (ωC)

Simplifying this equation, we find:

ω^2 = 1 / (LC)

Now, we know that the angular frequency ω is related to the frequency f by the equation:

ω = 2πf

We can substitute this into the equation above:

(2πf)^2 = 1 / (LC)

Now, we can rearrange this equation to solve for the frequency f:

f = 1 / (2π√(LC))

Since the frequency is given by f = 1 / T, where T is the period of the waveform, we can rewrite the equation as:

T = 2π√(LC)

This equation represents the period of the waveform that will maximize the current in the circuit. The largest current will flow when the period T is minimized.

To find the output voltage that produces this period T, we need to solve for Vm. However, without more information about the circuit or the desired current, we cannot determine the exact value of Vm.

In summary, to find the output voltage for the generator that produces the largest current in the circuit, you would need to calculate the period of the waveform using the equation T = 2π√(LC), and then use that period to determine the necessary output voltage.