LC Circuit Analysis and Waveforms

The video tutorial explains the derivation of the current expression in an LC circuit, using specific values for inductance and capacitance. It demonstrates the calculation of current and voltage, showing how they form sinusoidal waves. The tutorial also highlights the relationship between current and voltage, illustrating their phase difference through plots.

What is the expression for the current in an LC circuit in terms of capacitance, inductance, and starting voltage?

• i = sqrt(L/C) * V0 * sin(ω0t)

• i = sqrt(C/L) * V0 * sin(ω0t)

• i = sqrt(C*L) * V0 * sin(ω0t)

• i = sqrt(1/(C*L)) * V0 * sin(ω0t)

In the specific example, what is the value of the natural frequency ω0?

• 1 rad/s

• 4 rad/s

• 3 rad/s

• 2 rad/s

What is the expression for the current i(t) in the specific example?

• i(t) = 5 sin(2t)

• i(t) = 10 sin(2t)

• i(t) = 5 cos(2t)

• i(t) = 10 cos(2t)

What is the maximum amplitude of the current in the plotted sine wave?

• 5 Amperes

• 2 Amperes

• 10 Amperes

• 15 Amperes

Which equation is used to derive the voltage across the inductor in the LC circuit?

• V = C * d²i/dt²

• V = L * d²i/dt²

• V = C * di/dt

• V = L * di/dt

What is the expression for the voltage v(t) in the LC circuit?

• v(t) = 5 cos(2t)

• v(t) = 5 sin(2t)

• v(t) = 10 sin(2t)

• v(t) = 10 cos(2t)

How does the voltage waveform compare to the current waveform in terms of phase?

• Voltage leads current by 90 degrees

• Voltage lags current by 90 degrees

• Voltage and current are in phase

• Voltage and current are out of phase by 180 degrees

What is the initial value of the voltage at time t=0?

• 10 Volts

• 15 Volts

• 5 Volts

• 0 Volts

What is the significance of the natural response in an LC circuit?

• It indicates the constant current and voltage over time.

• It represents the linear increase of current and voltage.

• It demonstrates the sinusoidal nature of current and voltage.

• It shows the exponential decay of current and voltage.

What is the relationship between the current and voltage waveforms in an LC circuit?

• Both are sine waves.

• Both are cosine waves.

• Current is a sine wave, and voltage is a cosine wave.

• Current is a cosine wave, and voltage is a sine wave.