Option 4 : ωL

__CONCEPT:__

- The device which stores magnetic energy in a magnetic field is called an inductor.
- A circuit that has the only inductor is known as a purely inductive circuit.

**Inductive reactance**: The resistance offered to the flow of current by an inductor is known as inductive reactance.- It is represented by XL.

- Inductive reactance (X
_{L}) = ω L

Alternating emf in the circuit is:

\(e={{e}_{o}}\sin \omega t\)

Where e0 = maximum potential, ω = angular frequency and t = time

__EXPLANATION__:

**Inductive reactance = ω L**

So option 4 is correct.

Option 1 : lags the voltage by π/2

__CONCEPT:__

- Inductors: The coils of wire that are wound around any ferromagnetic material (iron cored) or wound around a hollow tube that increase their inductive value are called inductors.
- The inductance (L) is measured in Henry (H) and the instantaneous voltage in volts.
- Rate of instantaneous voltage is given by (v = L di/dt)

__EXPLANATION:__

- The given diagram is a simple inductor circuit with alternating current.
- From the phaser diagram, the Inductor current lags inductor voltage by 90° = π/2.

- The plot of current and voltage for this very simple circuit:
- From the current and voltage wave diagram, Inductor current lags inductor voltage by 90°. So option 1 is correct.

- Inductor current lags inductor voltage by 90°.
- Capacitor voltage lags current by 90°.
- In Resister only circuit, Voltage and Current are in the same phase.
- Or we can say there is no lag between current and voltage.

Option 3 : 90°

__CONCEPT:__

- A circuit that has the only inductor is known as a purely inductive circuit.

__EXPLANATION:__

- Alternating emf in the circuit is

\(e={{e}_{o}}\sin \omega t\)

- Current in the inductive circuit is

\(I={{I}_{o}}\sin \left( \omega t-\frac{\pi }{2} \right)\)

- From above it is clear that
**voltage leads the current**by**π/2**or**90°**. Therefore option 3 is correct.

Option 4 : ωL

__CONCEPT:__

- The device which stores magnetic energy in a magnetic field is called an inductor.
- A circuit that has the only inductor is known as a purely inductive circuit.

**Inductive reactance**: The resistance offered to the flow of current by an inductor is known as inductive reactance.- It is represented by XL.

- Inductive reactance (X
_{L}) = ω L

Alternating emf in the circuit is:

\(e={{e}_{o}}\sin \omega t\)

Where e0 = maximum potential, ω = angular frequency and t = time

__EXPLANATION__:

**Inductive reactance = ω L**

So option 4 is correct.

Option 2 : 2 × 104 Ω

__CONCEPT:__

**Inductor**: The device which stores magnetic energy in a magnetic field is called an inductor.- A circuit that has the only inductor is known as a purely inductive circuit.

**Inductive reactance**: The resistance offered to the flow of current by an inductor is known as inductive reactance.- It is represented by XL.

Inductive reactance (XL) = ω L

- Alternating emf in the circuit is

\(e={{e}_{o}}\sin ω t\)

Where e0 = maximum potential, ω = angular frequency and t = time

__EXPLANATION__:

The relation between frequency (f) and angular frequency (ω) is given by:

ω = 2π f

Given that:

Frequency (f) = 104 Hz

Reactance (X_{L}) = ω L = 2π f L = 10^{4} Ω

Now f' = 2 × 104 Hz = 2f

**New Reactance (XL') = ω' L = 2π f' L = 4 π f L = 2 × X _{L} = 2 ×104 Ω**

Option 1 : lags the voltage by π/2

__CONCEPT:__

- Inductors: The coils of wire that are wound around any ferromagnetic material (iron cored) or wound around a hollow tube that increase their inductive value are called inductors.
- The inductance (L) is measured in Henry (H) and the instantaneous voltage in volts.
- Rate of instantaneous voltage is given by (v = L di/dt)

__EXPLANATION:__

- The given diagram is a simple inductor circuit with alternating current.
- From the phaser diagram, the Inductor current lags inductor voltage by 90° = π/2.

- The plot of current and voltage for this very simple circuit:
- From the current and voltage wave diagram, Inductor current lags inductor voltage by 90°. So option 1 is correct.

- Inductor current lags inductor voltage by 90°.
- Capacitor voltage lags current by 90°.
- In Resister only circuit, Voltage and Current are in the same phase.
- Or we can say there is no lag between current and voltage.

Option 1 : lags the voltage by π/2

**CONCEPT:**

**Inductors:**The coils of wire that are wound around any ferromagnetic material (iron cored) or wound around a hollow tube that increase their inductive value are called**inductors**.- The inductance (L) is measured in Henry (H) and the instantaneous voltage in volts.
- Rate of instantaneous voltage is given by (
**v = L di/dt**)

**EXPLANATION:**

- The given diagram is a simple inductor circuit with alternating current.
- From the phaser diagram,
**Inductor current lags inductor voltage by 90°.**

- From the phaser diagram,

**The plot of current and voltage**for this very simple circuit:- From the current and voltage wave diagram, Inductor current lags inductor voltage by 90°.

- So, the correct answer will be
**option 1**.

- Inductor current lags inductor voltage by 90°.
- Capacitor voltage lags current by 90°.
**In Resister only circuit,**Voltage and Current are in the same phase.- Or we can say there is no lag between current and voltage.

Option 3 : 90°

__CONCEPT:__

- A circuit that has the only inductor is known as a purely inductive circuit.

__EXPLANATION:__

- Alternating emf in the circuit is

\(e={{e}_{o}}\sin \omega t\)

- Current in the inductive circuit is

\(I={{I}_{o}}\sin \left( \omega t-\frac{\pi }{2} \right)\)

- From above it is clear that
**voltage leads the current**by**π/2**or**90°**. Therefore option 3 is correct.

Option 2 : π/2

__CONCEPT__:

- Wattless current: The current in AC circuit is said to be
**wattless current**if the average power consumed in such circuit corresponds to zero and such current is also called**idle current**.

The average power of an AC circuit is given by:

Pav = ErmsIrms cos ϕ

The current Irms can be resolved into two components i.e. along with **parallel and perpendicular components**.

- The Component Irms cosϕ is along Erms . Here the phase angle between Irms cosϕ and Erms is zero.

Pav = Erms (Irms cos ϕ) cos 0 = Erms Irms cos ϕ

- The Component Irms sinϕ is normal to Erms . Here the phase angle between Irms sinϕ and Erms is π/2.

Pav = Erms (Irms sin ϕ) \(\cos \frac{\pi }{2}\) = 0

- We call the component Irms sin ϕ as the idle or wattles current because it does not consume any power in a.c. circuit.

__EXPLANATION__:

- Component Irms sinϕ is normal to Erms . As the phase angle between Irms sinϕ and Erms is π/2.

Pav = Erms (Irms sin ϕ) \(\cos \frac{\pi }{2}\) = 0

- We call the component Irms sin ϕ as the idle or wattles current because it does not consume any power in a.c. circuit. This happens in a purely inductive or capacitive circuit in which
**current and voltage differ by a phase difference of π /2**. - Hence option 2 is correct.

**NOTE:**

- The wattless current is possible in a circuit where resistance is zero.

Option 3 : 20 A

__CONCEPT:__

Inductive reactance:

- The inductive reactance is the opposition offered by the inductor in an AC circuit to the flow of ac current.
- Its SI unit is Ohm(Ω).
- The inductive reactance is given as,

⇒ XL = 2πfL

Where f = frequency of ac current and L = self-inductance of the coil

Impedance:

- Impedance is essentially everything that obstructs the flow of electrons within an electrical circuit.
- For a pure inductor, the inductive reactance is equal to the impedance.

AC voltage applied to an inductor:

- When an AC voltage is applied to an inductor, the current in the circuit is given as,

\(⇒ I=\frac{V}{X_L}\)

- In a pure inductor circuit, the current reaches its maximum value later than the voltage by one-fourth of a period.

__CALCULATION:__

Given V_{rms} = 220 V, L = 35 mH = 35×10-3 H, and f = 50 Hz

- We know that the inductive reactance is given as,

⇒ XL = 2πfL

\(⇒ X_L=\frac{2×22×50×35\times10^{-3}}{7}\)

⇒ XL = 11 Ω -----(1)

When an AC voltage is applied to an inductor, the current in the circuit is given as,

\(⇒ I=\frac{V}{X_L}\) -----(2)

By equation 1 and equation 2, the rms current in the circuit is given as,

\(⇒ I_{rms}=\frac{V_{rms}}{X_L}\)

\(⇒ I_{rms}=\frac{220}{11}\)

⇒ I_{rms} = 20 A

- Hence option 3 is correct.