ALTERNATING CURRENT
Very Short Question Answers
Q1. A transformer converts 200v ac into 2000ac.Calculate the number of turns in the secondary if the primary has 10 turns.
Ans. $N_{s} = \frac{V_{s}}{V_{p} ×N_{p}} = 2000/200 ×10 = 100 $
$ ∴Ns = 100 turns$
Q2. What type of transformer is used in a 6V bed lamp?
Ans. Step – down transformer
Q3. What is the phenomenon involved in the working of a transformer?
Ans. Mutual induction
Q4. What is the transformerratio?
Ans. The ratio between the number of turns in secondary coil and the number of turns in primary coil is called transformer ratio.
Transformer ratio (k) $=\frac{N_{s}}{N_{p}} = \frac{V_{s}}{V_{p}}$
Q5. Write the expression for the reactance of i ) an inductor and ii) a capacitor ?
Ans. $1)\:\; X_{L} = \:ω L \:\:\:2) X_{C} = \:1/ωC$
Q6. What is the phase difference between ac emf and current in the following: pure resistor, pure inductor and pure capacitor.
Ans. Pure resistor, phase difference is zero
Pure inductor, phase difference is $π/2$
Pure capacitor, phase difference is $π/2$
Q7. Define power factor. On which factors does the power factor depend?
Ans. Theaverage power over a complete cycle is $ P = VI\: cosϕ$ ( or )$ P= I ^{2} Z\, cosϕ $ in this, The term $cosϕ$ is called power factor. It depends on phase difference $\phi$ between current and voltage.
Q8. What is meant by wattless component of current?
Ans. When $cosϕ=0$ and no power so dissipated even though a current is flowing in the circuit. This is called wattles component of current.
Q9. When does a LCR series circuit has minimum impedance?
Ans. When $X_{L}= X_{C }\:\, , \:\, ω L = 1/ωC$
Q10. What is the phase difference between voltage and current when the power factor in LCR series circuit is unity?
Ans. If the power factor $cosϕ=1$.Then phase difference between voltage and current $ϕ=0$
Q11. What is step-up transformer How it differences from step-down transformer.
Ans. If the secondary coil has a more number of turns than the primary is called step-up transformer. $ N_{S}>N_{P}$.
If the primary coil has more turns than the secondary is called step – down transformer. $N_{S}<N_{P}$
Short Question Answers
Q1. Obtain an expression for the current through an inductor when an AC emf is applied.
Q2. Obtain an expression for the current in a capacitor when an AC emf is applied.
Q3. State the principle on which a transformer works. Describe the working of a transformer with necessary theory.
Long Question Answers
Q1. Obtain an expression for impedance and current in series LCR circuit. Deduce an expression for the resonating frequency of an LCR series resonating circuit.
Problems Question Answers
Q1. An ideal inductor (no internal resistance for the coil) of 20 mH is connected in series with an AC ammeter to an AC source whose emf is given by e = 20?2 sin(200t + x/3) V. where t is in seconds. Find the reading of the ammeter?
Q2. The instantaneous current and instantaneous voltage across a series circuit containing resistance and inductance are given by t = ?2 sin(100t - ?/4) A and v = 40 sin(100t) V. Calculate the resistance?
Q3. In an AC circuit, a condenser, a resistor and a pure inductor are connected in series across an alternator (AC generator). If the voltages across them are 20 V, 35 V and 20 V respectively, find the voltage supplied by the alternator.
Q4. An AC circuit contains a resistance R. an inductance L and a capacitance C connected in series across an alternator of constant voltage and variable frequency. At resonant frequency, it is found that the inductive reactance, the capacitive reactance and the resistance are equal and the current in the circuit is . Find the current in the circuit at a frequency twice that of the resonant frequency.
Q5. A series resonant circuit contains L,. R, and C,. The resonant frequency is f. Another series resonant circuit contains L, R and C. The resonant frequency is also f. If these two circuits are connected in series, calculate the resonant frequency.
Q6. In a series LCR circuit R= 200 W and the voltage and the frequency of the mains supply is 200 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 45°. On taking out the inductor from the circuit the current leads the voltage by 45°. Calculate the power dissipated in the LCR circuit.
Q7. The primary of a transformer with primary to secondary turns ratio of 1:2, is connected to an alternator of voltage 200 V. A current of 4 A is flowing though the primary coil. Assuming that the transformer has no losses. find the secondary voltage and current are respectively.