AC 2

Question 1

POWER IN AC CIRCUIT: THE POWER FACTOR

Answer 1

P=VI cos p

vi - virtual factor
cos phi - power factor

Question 2

power in each case
i) purely resistive circuit
ii) purely inductivecapacitive circuit
iii) LCR circuit
iv) lcr at resonance

Answer 2

Case (i) Case (i) Case (i) Resistive circuit: If the circuit contains only pure R, it is called
resistive. In that case φ = 0, cos φ =1.Thereis maximum power dissipation.

Case (ii) Case (ii) Case (ii) Purely inductive or capacitive circuit: If the circuit contains
only an inductor or capacitor, we know that the phase difference between
voltage and current is π/2. Therefore, cos φ = 0, and no power is dissipated
even though a current is flowing in the circuit. This current is sometimes
referred to as wattless current.

Case (iii) Case (iii) Case (iii) LCR series circuit: In an LCR series circuit, power dissipated is
given by Eq. (7.30) where φ = tan–1 (Xc– XL
)/ R. So, φ may be non-zero in
a RL or RC or RCL circuit. Even in such cases, power is dissipated only in
the resistor.

Case (iv) Case (iv)Case (iv) Power dissipated at resonance in LCR circuit: At resonance
Xc
– XL
= 0, and φ = 0. Therefore, cosφ = 1 and P = I
2Z = I
2 R. That is,
maximum power is dissipated in a circuit (through R) at resonance.

Question 3

) For circuits used for transporting electric power, a
low power factor implies large power loss in transmission. Explain.

Answer 3

We know that P = I V cosφ where cosφ is the power factor.
To supply a given power at a given voltage, if cosφ is small, we have to
increase current accordingly. But this will lead to large power loss
(I
2R) in transmission.

Question 4

At an airport, a person is made to walk through the
doorway of a metal detector, for security reasons. If she/he is carrying
anything made of metal, the metal detector emits a sound. On what
principle does this detector work?

Answer 4

The metal detector works on the principle of resonance in
ac circuits. When you walk through a metal detector, you are,
in fact, walking through a coil of many turns. The coil is connected to
a capacitor tuned so that the circuit is in resonance. When
you walk through with metal in your pocket, the impedance of the
circuit changes – resulting in significant change in current in the
circuit. This change in current is detected and the electronic circuitry
causes a sound to be emitted as an alarm.