Electromagnetic Oscillations and Alternating Current MCQ Quiz - Objective Question with Answer for Electromagnetic Oscillations and Alternating Current - Download Free PDF

Correct option is: (2) 7.8 A and 45°

X_L = 45 W, X_C = 25 W, R = 20 W

⇒ I = 220 / √((X_L − X_C)² + R²) = 220 / √((45 − 25)² + 20²)

⇒ = 220 / (2√2) = 11 / √2 = 7.779 A

⇒ tan φ = (X_L − X_C) / R = (45 − 25) / 20 = 1

⇒ φ = 45°

Calculation:

In circuit (p): Under steady state, the capacitor will act as an infinite impedance and the inductor will act as a zero impedance. Thus:

I = 0

V₁ = 0

V₂ = V

In circuit (q): The inductor will act as zero resistance in steady state, giving us:

I = V / R = V / 2

V₁ = 0

V₂ = V

In circuit (r): The inductive reactance X_L and total impedance Z are:

X_L = ωL = 2πνL = 1.88 Ω

Z = √(X_L² + R²) = 2.75 Ω

Thus,

I = V / Z ≠ 0

V₁ = X_LI = 1.88I

V₂ = RI = 2I

V₂ > V₁

In circuit (s): Inductive reactance X_L, capacitive reactance X_C, and impedance Z are:

X_L = 1.88 Ω

X_C = 1 / (ωC) = 1061 Ω

Z = X_C − X_L = 1059 Ω

So the current is:

I = V / Z ≠ 0

V₁ = X_LI = 1.88I

V₂ = X_CI = 1061I

V₂ > V₁

Answer:  A → (r, s), B → (q, r, s), C → (p, q), D → (q, r, s )

As \(\omega\) increases, \(Z\) decreases.

Hence, bulb will glow brighter.

CONCEPT:

• Voltage in AC: In an AC voltage source, the voltage of the source keeps changing with time and is defined as

V = V₀ sin ωt

where V is the voltage at any time t, V₀ is the max value of voltage, and ω is the angular frequency.

• With AC source capacitance, In a series combination of a resistor (R), an inductance (L)

Inductance Reactanceis defined as

 \(X_L = ω L=2\pi fL\)

Where ω is the angular frequency, ƒ is the frequency in Hertz, C is the AC capacitance in Farads, and X_L is the Inductive Reactance in Ohms,.

Overall Impedance (Z) in a series combination of a resistor (R), an inductance (L):

\(Z = \sqrt{R^2 + {ω L}^2}\)

where R is resistance and ωL is Inductance reactance.

• Power Factor: The power factor of series-connected L and R circuit in AC voltage is

cos ϕ = R/Z

where R is resistance and Z is overall impedance.​

CALCULATION:

Given that L = 0.5H and R = 500 Ω

V = 100√2 sin (1000 t)

compare it with standard equation. V = V0 sin ωt

ω = 1000

\(X_L = ω L=1000 \times 0.5=500 \Omega\)

\(Z = \sqrt{R^2 + {ω L}^2} = \sqrt{500^2 + {500}^2}\)

\(Z = 500\sqrt2 \Omega\)

Power factor cos ϕ = R/Z

cos ϕ = \({500 \over500\sqrt2} ={ 1\over \sqrt2}\)

So the correct answer is option 1.

Calculation:

\(Z=\sqrt{R^2+(\omega L-\dfrac{1}{\omega C})}\)

\(=\sqrt{(300)^2+\left(1000\times 0.9-\dfrac{1}{1000\times 2\times 10^{-6}}\right)^2}\)

\(Z=\sqrt{(300)^2+(400)^2}\Rightarrow 500\Omega \)

The correct option is (a)

The correct answer is  Periodically.

Key Points

CONCEPT:

• The electric current flows in two ways: Alternating current and Direct Current.
  • Direct current flows only in one direction.

• Alternating current: The electric current whose direction changes periodically is called electric current.

• Alternating current reverses its direction periodically.
• It also changes its magnitude periodically because of the induced electromagnetic force.
• For Alternating current both magnitude and direction change. The frequency of the alternating current in the Indian power supply is 50 Hz. The time period is 1/50 = 20 msec.

EXPLANATION:

• In Alternating Current (AC), the direction and magnitude of the current vary periodically. So option 2 is correct.

CONCEPT:

Transformer:

• An electrical device that is used to transfer electrical energy from one electrical circuit to another is called a transformer.

There are two types of transformer:

1. Step-up transformer:

• The transformer which increases the potential is called a step-up transformer.
• The number of turns in the secondary coil is more than that in the primary coil.

2.Step-down transformer:

• The transformer which decreases the potential is called a step-down transformer.
• The number of turns in the secondary coil is less than that in the primary coil.

EXPLANATION:

• As in the step-up transformer, the number of coils in the secondary coil is more than that in the primary coil. So the electrical potential increases.
• Hence step-up transformer is used for increasing the voltage/potential. So option 4 is correct.

• In step-up transformer, the current in the secondary coil is less than that in the primary coil.

The correct answer is Minimize eddy current loss.

• Transformer cores are laminated in order to minimize core loss.
• By providing laminations, the area of each part gets reduced and hence resistance will get very high which limits the eddy current to a minimum value, and hence eddy current losses get reduced. 
• The laminations provide small gaps between the plates. As it is easier for magnetic flux to flow through iron than air or coil, the stray flux or leakage flux that can cause core losses is minimized.

CONCEPT:

• The ac circuit containing the capacitor, resistor, and the inductor is called an LCR circuit.
• For a series LCR circuit, the total potential difference of the circuit is given by:

\(V = \sqrt {{V_R^2} + {{\left( {{V_L} - {V_C}} \right)}^2}} \)

Where VR = potential difference across R, VL =  potential difference across L and VC =  potential difference across C

• For a series LCR circuit, Impedance (Z) of the circuit is given by:

\(\)\(Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} \)
Where R = resistance, XL =induvtive reactance and XC = capacitive reactive

CALCULATION:

• For a series LCR circuit, Impedance (Z) of the circuit is given by:

\(\)\(\Rightarrow Z = \sqrt {{R^2} + {{\left( {{X_L} - {X_C}} \right)}^2}} \)

• Inductive reactance,

⇒ XL = Lω  

• Capacitive reactance

​\(\Rightarrow X_c=\frac{1}{C\omega}\)

• Resonance will take place when XL = X_C.

​⇒ XL = X_C

\(\Rightarrow L\omega =\frac{1}{C\omega}\)

CONCEPT:

Transformer:

An electrical device that is used to transfer electrical energy from one electrical circuit to another is called a transformer.

There are two types of transformer:

Step-up transformer:

• The transformer which increases the potential is called a step-up transformer.
• The number of turns in the secondary coil is more than that in the primary coil.

Step-down transformer:

• The transformer which decreases the potential is called a step-down transformer.
• The number of turns in the secondary coil is less than that in the primary coil.

EXPLANATION:

• As in the step-up transformer, the number of coils in the secondary coil is more than that in the primary coil. So the electrical potential increases.
• A step-up transformer converts low voltage at high current into a high voltage at low current. So option 4 is correct.

• In a step-up transformer, the current in the secondary coil is less than that in the primary coil.

• The secondary coil is made of thin insulated wire while the primary coil is made of thick insulated wire.

CONCEPT:

• Root mean square value of Alternating current (I_rms): The value of steady current, which would generate the same amount of heat in a given resistance in a given time, as is done by the alternating current. when passed through the same resistance for the same time.
  • The r.m.s. value is also called effective value or virtual value of alternating current.

The relation between the peak value of the alternating current value of current (Io) and r.m.s. value of the current is given as:
\({I_{rms}} = \frac{{{I_o}}}{{√ 2 }}\)

CALCULATION:

Given that:

Peak current (I₀) = 2√2 A

\({I_{rms}} = \frac{{{I_o}}}{{√ 2 }}\)

\({I_{rms}} = \frac{{{2\sqrt2}}}{{√ 2 }} = 2 A\)

The rms value is 2 A.

Concept:

The power factor of the inductor has lagging nature, whereas for capacitor its leading.

For a pure inductor \(\phi = {90^0}\) (The angle between voltage and current)

This shows that if we plot voltage vs current graph the output signal will be lagging by phase angle π/2

The given figure shows the power factor (ϕ) for pure R, L and C circuit 

Explanation:

From the above explanation, we can see that for a pure capacitance circuit if AC voltage of v = vm sinωt then the driven current in the capacitor will be 

I = im sin(ωt + ϕ) 

Now as mentioned for pure inductor phase angle will be lagging by 90° or π/2.

i.e., ϕ = π/2  ⇒ i = im sin (ωt + π/2)

Concept:

• A transformer is an electrical device which transfers electrical energy from one circuit to another
• It works based on the principle of electromagnetic induction
• It is used for increasing or decreasing the amount of voltage or current as per our requirement based on these transformers are classified into two types step-up (increasing) or step-down (decreasing) transformer.

There are two types of transformer:

1. Step-up transformer:

• The transformer which increases the potential is called a step-up transformer.
• The number of turns in the secondary coil is more than that in the primary coil.

2.Step-down transformer:

• The transformer which decreases the potential is called a step-down transformer.
• The number of turns in the secondary coil is less than that in the primary coil.

Explanation:

As in an ideal transformer, there is no loss of power i.e.

Pout = Pin

So, VsIs = VpIp

\(\therefore \frac{{{V_s}}}{{{V_p}}} = \frac{{{N_s}}}{{{N_P}}} = \frac{{{I_P}}}{{{I_S}}}\)

Where Ns = number of turns of the secondary coil, NP = number of turns of the primary coil, Vs = Voltage secondary coil, VP = Voltage primary coil, Is = Current in the secondary coil and IP = current in the primary coil.

In Step up transformer voltage is increased So, the current will be reduced. As there is no loss in power.

Additional Information

• A transformer can be used to either increase or decrease the voltage of a circuit.
• In other words, it can either step up (increase) or step down (decrease) the voltage.
• A transformer is necessary because sometimes the voltage requirements of different appliances are variable.

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. 

CONCEPT:

Alternating current: 

• An alternating current can be defined as a current that changes its magnitude and polarity at a regular interval of time.

RMS value of current: 

• RMS value of current is defined as the square root of the mean of the square of AC current for 1 complete cycle.
  • It is equal to that value of DC current which generates the same heating effect as the AC current.

​\(⇒ I_{rms}= \frac{I_{o}}{\sqrt{2}}\)     -----(1)

Where I_o = peak value of AC current

CALCULATION:

​Given -  I = 2cos(ωt+θ)

• The value of I will be maximum when cos(ωt+θ) is maximum,
• The maximum value of cos(ωt+θ) = 1

Therefore,

⇒ I_o = 2A

So,

\(⇒ I_{rms}= \frac{I_{o}}{\sqrt{2}}=\frac{2}{\sqrt{2}}=\sqrt{2}A\)

• Hence, option 1 is correct.