Inductor blocks AC but allows DC to flow

Why Inductor blocks AC but allows DC to flow?

We know,

Inductive reactance, X_L = 2ΠfL
For DC supply the frequency f is zero. So reactance X_L = 0 and it allows DC to flow. But for AC supply there is a frequency. So the reactance X_L is not zero and it blocks AC.

  

Inductor blocks AC while allowing DC to flow because it only resists the change in current. 

_{The equation of inductor is, V = L di/dt}

Capacitor blocks DC but allows AC to flow

Why Capacitor blocks DC but allows AC to flow?

 We can explain this fact mainly in two ways:

• We know,

Capacitive reactance, X_c = 1/ 2ΠfC

For DC supply, frequency f is zero. So the reactance becomes infinity. As a result it blocks DC. But for AC supply the frequency f is not zero. So the reactance is not infinity and it allows some AC to flow.

• We know,

Current through capacitor, I = C dv/dt

As the voltage does not change during DC supply,

dv/dt = 0

So Current through capacitor, I = 0

It means for DC supply capacitor blocks it. But for AC supply dv/dt is not equal to zero. So surely some certain value of I passes through the capacitor.

Role of capacitor in a ceiling fan

What is the role of capacitor in a ceiling fan?

We normally use 1-ɸ induction motor in a ceiling fan. In a 1-ɸ induction motor, stator produces a non rotating magnetic field. This is because the coil excited by the 1-ɸ current produces two counter rotating magnetic fields. They are of alternating polarity. So they cancel each other at 0°, 90°, 180°, -90°, -180° and hence no starting torque is developed.

 

So in order to generate the starting torque we have to split the phase in two. This work is done by using a capacitor. 

The configuration is:

• Two windings (W₁ and W₂)
• A centrifugal switch and
• A capacitor

The capacitor provides a phase shift to the current flowing in W₁ and we get an induction motor like a 2-ɸ induction motor having uniformly rotating magnetic flux of constant value.

When the motor is almost up to the speed, the switch opens disconnecting W₁ and the capacitor.

I am giving an explanation why a 2-ɸ or 3-ɸ induction motor can have uniformly rotating magnetic flux of constant value.

Suppose a 2-ɸ, 2-pole induction motor is connected with a 2-ɸ, 3 wire system.

Let,

ɸ₁ and ɸ₂ are the two fluxes for the two phases.

ɸ_r = The vector sum of two fluxes.

 

When θ = 0°, ɸ₁ = 0  and  ɸ₂ = maximum. So, ɸ_r = ɸ_m (negative)

When θ = 45°, ɸ₁ = ɸ_m/√2 (Positive), ɸ₂ = ɸ_m/√2 (negative)

            So, ɸ_r = √ [(ɸ_m/√2)² + (ɸ_m/√2)²] = ɸ_m

When θ = 90°, ɸ₂ = 0  and  ɸ₁ = ɸ_m (positive). So, ɸ_r = ɸ_m

When θ = 135°, ɸ₁ = ɸ_m/√2 (Positive), ɸ₂ = ɸ_m/√2 (positive)

            So, ɸ_r = √ [(ɸ_m/√2)² + (ɸ_m/√2)²] = ɸ_m

When θ = 180°, ɸ₁ = 0  and  ɸ₂ = ɸ_m (positive). So, ɸ_r = ɸ_m

So the magnitude of the resultant flux is constant and equal to the maximum flux due to either phase. The resultant flux rotates the rotor of the motor at synchronous speed.