Question

The value of alternating emf \(E\) in the given ckt will be. (a) \(100 \mathrm{~V}\) (b) \(20 \mathrm{~V}\) (c) \(220 \mathrm{~V}\) (d) \(140 \mathrm{~V}\)

Short answer

Since no specific information about the circuit is provided, we cannot determine the exact value of the alternating emf "E". However, once the details of the circuit are given, following the steps outlined above will help to find the correct answer from the given options.

Step-by-step solution

Understand the circuit components and parameters

First, we need to gather information about the different components of the circuit and their parameters (such as resistances, inductances, capacitances, etc.) from the given problem statement. Since no information is provided about the circuit, we'll have to assume that there is a series RL or RC circuit with known values for the resistance, inductor, and capacitor.

Determine the phasor representation of the voltage and current

Next, we need to represent the voltage and current phasor quantities using complex numbers. For a series RL or RC circuit, we can use the impedance (Z) for relating voltage and current. Impedance can be found by the formula: For RL circuit: \(Z = R + j{\omega}{L}\) For RC circuit: \(Z = R - \frac{j}{\omega}{C}\) Where R is the resistance, L is the inductance, C is the capacitance, j is the imaginary unit, and ω is the angular frequency of the alternating current.

Find the total voltage across the circuit

To find the total voltage across an RL or RC circuit, we can use Ohm's law: \(V = I \times Z\) where V is the total voltage, I is the current, and Z is the impedance.

Calculate the magnitude of the total voltage

To find the alternating emf "E," we need to calculate the magnitude of the total voltage. We can do this using the following equation for a complex number: \( \mathrm{Magnitude~of~Voltage} = |V| = \sqrt{\mathrm{Real~Part}^2 + \mathrm{Imaginary~Part}^2}\) Where Real Part and Imaginary Part are the real and imaginary components of the voltage complex number, respectively.

Compare the calculated magnitude to the given options

Finally, compare the calculated magnitude of the total voltage (|V|) to the four given options. The value that matches the calculated result will be the correct answer for the given problem. Without any specific information about the circuit, we can't provide a step-by-step solution for this problem. However, these steps can be followed once the necessary details are provided to arrive at the correct answer.