Question

In an LRC series circuit, the rms

.
voltage across the resistor is 30.0 V
across the capacitor it is 90.0 V, and
across the inductor it is 50.0 V. The
rms voltage of the source is​

Answer 1

To find the rms voltage of the source in an LRC series circuit, we can use the phasor diagram. By considering the rms voltages across the resistor, capacitor, and inductor, we can find the magnitude of the source voltage.

Step-by-step explanation:

In an LRC series circuit, the rms voltage across the resistor, capacitor, and inductor can be used to find the rms voltage of the source. In this case, the rms voltage across the resistor is 30.0 V, the rms voltage across the capacitor is 90.0 V, and the rms voltage across the inductor is 50.0 V. To find the rms voltage of the source, we need to consider the phasor diagram.

The phasor diagram is a graphical representation of the voltage phasors of the resistor, capacitor, inductor, and source. The phasor sum of the resistor, capacitor, and inductor voltages should add up to the source voltage. By using the Pythagorean theorem, we can determine the magnitude of the source voltage.

Magnitude of Source Voltage = sqrt((Voltage across Resistor)^2 + (Voltage across Capacitor)^2 + (Voltage across Inductor)^2)

Substituting the given values:

Magnitude of Source Voltage = sqrt((30.0 V)^2 + (90.0 V)^2 + (50.0 V)^2) = sqrt(900 + 8100 + 2500) = sqrt(11500) ≈ 107.06 V

Answer 2

In an LRC series circuit, the rms voltage across the resistor, capacitor, and inductor can be calculated using the formula V = IR. Given the rms voltages across each component, we can use the phasor diagram and the pythagorean theorem to find the resultant voltage of the source. The rms voltage of the source in this case is found to be 50.0 V.

Step-by-step explanation:

In an LRC series circuit, the rms voltage across the resistor, capacitor, and inductor can be determined using the equation V = IR, where V is the voltage, I is the current, and R is the resistance. In this case, we are given the rms voltages across each component:

• Resistor: 30.0 V
• Capacitor: 90.0 V
• Inductor: 50.0 V

To find the rms voltage of the source, we can consider the phasor diagram:

• The resistor voltage, VR, is in phase with the current, so it can be taken as the reference.
• The capacitor voltage, VC, leads the current by 90 degrees.
• The inductor voltage, VL, lags the current by 90 degrees.

Since the resistor voltage is in phase with the current, we can assume the current to be the same as the voltage, i.e., VR = IR = 30.0 V.

Using the pythagorean theorem, we can find the resultant voltage, VS, as:

VS^2 = VR^2 + (VC - VL)^2

VS = sqrt(VR^2 + (VC - VL)^2)

Plugging in the given values:

VS = sqrt((30.0 V)^2 + (90.0 V - 50.0 V)^2)

VS = sqrt(900 V^2 + 1600 V^2)

VS = sqrt(2500 V^2)

VS = 50.0 V

Therefore, the rms voltage of the source is 50.0 V.