Find the total voltage applied in a series RLC circuit when i=3mA, VL=30V, VC=18V and R=1000 ohms.

1
3.95V

2
32.67V

3
6.67V

4

51V

Question

Find the total voltage applied in a series RLC circuit when i=3mA, VL=30V, VC=18V and R=1000 ohms.13.95V232.67V36.67V451V

Answer

Here L0 is current
Z0 is impedence, we know that Z=E0÷L0 and power P=E0L0cos¢ by substuting kn options we get option 'd'

Answer

Given:
- Current, i = 3mA
- Inductive voltage, VL = 30V
- Capacitive voltage, VC = 18V
- Resistance, R = 1000 ohms

To find: Total voltage applied in the series RLC circuit

Solution:
To find the total voltage applied in the series RLC circuit, we need to consider the voltage across each component and the phase relationship between them.

Step 1: Finding the voltage across the resistor (VR)
In a series circuit, the voltage across each component adds up to the total voltage. Since the resistor is purely resistive, the voltage across it is in phase with the current. Therefore, VR = i * R = 3mA * 1000 ohms = 3V.

Step 2: Finding the total voltage (V)
The total voltage in a series RLC circuit is the vector sum of the voltage across the resistor (VR), inductor (VL), and capacitor (VC).

Since the voltages across the inductor and capacitor are given, we can directly add them to find the total reactive voltage (Vr):
Vr = VL - VC = 30V - 18V = 12V.

The total voltage (V) can be found using the Pythagorean theorem:
V = sqrt(VR^2 + Vr^2) = sqrt(3V^2 + 12V^2) = sqrt(9V^2 + 144V^2) = sqrt(153V^2) = 12.37V.

Answer:
The total voltage applied in the series RLC circuit is approximately 12.37V.

Answer

Explanation: Total voltage= VR+VL+VC.
VR=1000x3x10-3=3V.
Therefore, total voltage = 30+18+3=51V.

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