Alternating Current

The peak value of an alternating current is $I_0$. Its root mean square (rms) value ($I_{rms}$) is given by:

For a direct current (DC), the capacitive reactance ($X_C$) is:

In a purely inductive AC circuit, the phase difference between current and voltage is:

The resonant frequency ($f_r$) of a series LCR circuit is given by:

The current flowing in an AC circuit is called 'Wattless Current' when the phase difference between voltage and current is:

On which working principle does a transformer operate?

The core of a transformer is laminated to minimize energy loss caused by:

In India, the RMS voltage and frequency of the domestic AC supply are respectively:

If the RMS voltage of an AC supply is $220\text{ V}$, its peak voltage ($V_0$) is approximately:

At electrical resonance in a series LCR circuit, the impedance of the circuit is:

A transformer cannot be used to step up or step down:

If the phase difference between alternating voltage and current in an AC circuit is $\phi$, the power factor is:

What is meant by the root mean square (RMS) value of alternating current? State its relation with peak value.

Define Inductive Reactance ($X_L$). How does it depend on the frequency of alternating current?

What is Wattless Current? Under what condition does it flow in an AC circuit?

Define Power Factor of an AC circuit. What are its maximum and minimum values?

What is electrical resonance in a series LCR circuit? Write the formula for resonant frequency.

Why is alternating current (AC) preferred over direct current (DC) for long-distance transmission of electric power?

An AC voltage given by $V = 200 \sqrt{2} \sin(100 \pi t)$ is applied across a circuit. Find its peak voltage and frequency.

Explain what a Choke Coil is and why it is preferred over a resistor to control current in an AC circuit.

Explain the concept of Root Mean Square (RMS) value of alternating current and derive its relationship with the peak value ($I_0$).

What are Inductive Reactance ($X_L$) and Capacitive Reactance ($X_C$)? Explain how their values depend on the frequency of the alternating current.

Define Quality Factor (Q-factor) of a resonant series LCR circuit. State its physical significance and write down its mathematical expression.

Explain the working principle of a transformer. Why cannot a transformer be used to step up or step down Direct Current (DC) voltage?

What is meant by Wattless Current? Under what conditions does the current in an AC circuit become wattless?

Explain the concept of 'Wattless Current' in an alternating current (AC) circuit. Under what condition is the current in an AC circuit said to be purely wattless?

What is electrical resonance in a series LCR circuit? Derive the expression for the resonant frequency of a series LCR circuit.

What is a Transformer? State its operating principle and explain any three major energy losses that occur in a real transformer, along with methods to minimize them.

Derive an expression for the impedance ($Z$) and phase angle ($ \phi$) of a series LCR alternating current circuit using the phasor diagram method. Also, define electrical resonance, derive the expression for the resonant frequency, and explain the Quality Factor ($Q$-factor) of the circuit.

What is a transformer? Explain its principle, construction, and working mechanism. Describe the main types of energy losses in a real transformer and explain how each loss can be minimized.

Derive an expression for the total impedance ($Z$) and phase angle ($\phi$) of a series LCR circuit connected to an alternating voltage source $V = V_0 \sin(\omega t)$ using the phasor diagram method. Also, derive the condition for electrical resonance and write the expression for the resonant frequency.

Explain the principle, construction, and working of a Transformer with a labeled diagrammatic representation. Also, discuss four major energy losses that occur in a real transformer along with methods used to minimize them.

What is a series LCR alternating current circuit? Derive the expression for the total impedance ($Z$), phase angle ($\phi$) between voltage and current, and the resonant frequency ($f_r$) of the circuit using a phasor diagram.

Explain the principle, construction, and working of a transformer. Differentiate between a step-up and a step-down transformer.

Numerical Problem: A step-down transformer converts $2200\text{ V}$ to $220\text{ V}$. The primary coil has $5000$ turns. Calculate:

1. The number of turns in the secondary coil.
2. The output power and secondary current if the efficiency of the transformer is $90%$ and the primary current is $2\text{ A}$.

(a) Explain the working of a series $LCR$ alternating current circuit. Derive the expressions for the impedance ($Z$), phase angle ($\phi$), and resonant frequency ($f_r$) using the phasor diagram method.

(b) A series $LCR$ circuit consists of a resistor $R = 10\ \Omega$, an inductor $L = 20\text{ mH}$, and a capacitor $C = 100\ \mu\text{F}$ connected across an AC voltage source given by $V = 200 \sin(100\pi t)\text{ V}$. Calculate:

1. The resonant frequency of the circuit.
2. The impedance of the circuit at resonance.
3. The peak current ($I_0$) flowing through the circuit at resonance.