The element involved can be determined by comparing the phase angles of the voltage and current. In a resistor, the voltage and current are in phase (0° phase difference). In an inductor, the voltage leads the current by 90°. In a capacitor, the current leads the voltage by 90°.

In this case, the phase of the current i(t) is leading the phase of the voltage v(t) by 90° (150° - 60° = 90°). Therefore, the element involved is a capacitor.

The value of the capacitor can be found using the formula for the reactance of a capacitor, Xc = 1/(2πfC), where f is the frequency and C is the capacitance.

First, we need to find the frequency. The angular frequency ω is given in the equations for v(t) and i(t) as 157 rad/s. The frequency f in Hz can be found by dividing the angular frequency by 2π, so f = ω/(2π) = 157/(2π) = 25 Hz.

Next, we can find the reactance Xc from Ohm's law, V = I*Xc. Rearranging for Xc gives Xc = V/I = 60V/5A = 12 ohms.

Finally, we can find the capacitance C by rearranging the formula for Xc: C = 1/(2πfXc) = 1/(2π*25Hz*12ohms) = 531 µF.

So, the element is a capacitor with a value of 531 µF.

Question

The element involved can be determined by comparing the phase angles of the voltage and current. In a resistor, the voltage and current are in phase (0° phase difference). In an inductor, the voltage leads the current by 90°. In a capacitor, the current leads the voltage by 90°.

In this case, the phase of the current i(t) is leading the phase of the voltage v(t) by 90° (150° - 60° = 90°). Therefore, the element involved is a capacitor.

The value of the capacitor can be found using the formula for the reactance of a capacitor, Xc = 1/(2πfC), where f is the frequency and C is the capacitance.

First, we need to find the frequency. The angular frequency ω is given in the equations for v(t) and i(t) as 157 rad/s. The frequency f in Hz can be found by dividing the angular frequency by 2π, so f = ω/(2π) = 157/(2π) = 25 Hz.

Next, we can find the reactance Xc from Ohm's law, V = I*Xc. Rearranging for Xc gives Xc = V/I = 60V/5A = 12 ohms.

Finally, we can find the capacitance C by rearranging the formula for Xc: C = 1/(2πfXc) = 1/(2π*25Hz*12ohms) = 531 µF.

So, the element is a capacitor with a value of 531 µF.

Knowee AI · Accepted Answer

The element involved can be determined by comparing the phase angles of the voltage and current. In a resistor, the voltage and current are in phase (0° phase difference). In an inductor, the voltage leads the current by 90°. In a capacitor, the current leads the voltage by 90°.

In this case, the phase of the current i(t) is leading the phase of the voltage v(t) by 90° (150° - 60° = 90°). Therefore, the element involved is a capacitor.

The value of the capacitor can be found using the formula for the reactance of a capacitor, Xc = 1/(2πfC), where f is the frequency and C is the capacitance.

First, we need to find the frequency. The angular frequency ω is given in the equations for v(t) and i(t) as 157 rad/s. The frequency f in Hz can be found by dividing the angular frequency by 2π, so f = ω/(2π) = 157/(2π) = 25 Hz.

Next, we can find the reactance Xc from Ohm's law, V = I*Xc. Rearranging for Xc gives Xc = V/I = 60V/5A = 12 ohms.

Finally, we can find the capacitance C by rearranging the formula for Xc: C = 1/(2πfXc) = 1/(2π*25Hz*12ohms) = 531 µF.

So, the element is a capacitor with a value of 531 µF.

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