An inductor L of inductance is connected in series with a bulb B and an ac source. How would brightness of the bulb change when
(i) number of turns in the inductor is reduced,
(ii) an iron rod is inserted in the inductor and
(iii) a capacitor of reactance is inserted in series in the circuit. Justify your answer in each case.
(i) number of turns in the inductor is reduced,
(ii) an iron rod is inserted in the inductor and
(iii) a capacitor of reactance is inserted in series in the circuit. Justify your answer in each case.
(i)Increases : = ωL
As number of turns decreases, L decreases, hence current through bulb increases / voltage across bulb increases.
∴ Brightness increases.
(ii) Decreases :
Iron rod increases the inductance, which increases , hence current through the bulb decreases / voltage across bulb decreases.
∴ Brightness decreases.
(iii) Increases :
Under this condition () the current through the bulb will become maximum / increase.
∴ Brightness increases.
As number of turns decreases, L decreases, hence current through bulb increases / voltage across bulb increases.
∴ Brightness increases.
(ii) Decreases :
Iron rod increases the inductance, which increases , hence current through the bulb decreases / voltage across bulb decreases.
∴ Brightness decreases.
(iii) Increases :
Under this condition () the current through the bulb will become maximum / increase.
∴ Brightness increases.
A source of ac voltage V = V₀ sin ωt, is connected across a pure inductor of inductance L. Derive the expressions for the instantaneous current in the circuit. Show that average power dissipated in the circuit is zero.
For an ideal conductor, connected across a sinusoidal ac voltage source. State which one of the following quantity is zero :
(i) Instantaneous power
(ii) Average power over full cycle of the ac voltage source.
A source of ac voltage V = V₀ sin ωt is connected to a series combination of a resistor ‘R’ and a capacitor ‘C’. Draw the phasor diagram and use it to obtain the expression for
(i) impedance of the circuit and
(ii) phase angle.
A lamp is connected in series with a capacitor. Predict your observation for dc and ac connections. What happens in each if the capacitance of the capacitor is reduced ?
A device ‘X’ is connected to an ac source V = V₀ sin(ωt). The variation of voltage, current and power in one complete cycle is shown in the following figure.
(i) Which curve shows power consumption over a full cycle?
(ii) Identify the device ‘X’.
A circuit containing an 80 mH inductor and a 250 µF capacitor in series connected to a 240 V,100 rad/s supply. The resistance of the circuit is negligible.
(i) Obtain rms value of current.
(ii) What is the total average power consumed by the circuit ?
In a series LR circuit = R and power factor of the circuit is P₁. When capacitor with capacitance C such that = is put in series, the power factor becomes P₂. Calculate P₁ / P₂.
(i) The potential difference applied across a given resistor is altered so that the heat produced per second increases by a factor of 9. By what factor does the applied potential difference change ?
(ii) In the figure shown, an ammeter A and a resistor of 4 W are connected to the terminals of the source. The emf of the source is 12 V having an internal resistance of 2 W. Calculate the voltmeter and ammeter readings.
What is relaxation time ? Derive an expression for resistivity of a wire in terms of number density of free electrons and relaxation time.
Derive an expression for electric field of a dipole at a point on the equatorial plane of the dipole. How does the field vary at large distances?
A circuit containing an 80 mH inductor and a 250 µF capacitor in series connected to a 240 V,100 rad/s supply. The resistance of the circuit is negligible.
(i) Obtain rms value of current.
(ii) What is the total average power consumed by the circuit ?
The temperature coefficient of resistivity, for two materials A and B, are 0.0031 / °C and 0.0068 / °C respectively.
Two resistors R1 and R2, made from materials A and B, respectively, have resistances of 200 Ω and 100 Ω at 0°C. Show on a diagram, the 'colour code', of a carbon resistor, that would have a resistance
equal to the series combination of R1 and R2, at a temperature of 100°C.
(Neglect the ring corresponding to the tolerance of the carbon resistor).
First a set of n equal resistors of R each is connected in series to a battery of emf E and internal resistance R. A current I is observed to flow. Then the n resistors are connected in parallel to the same battery. It is observed that the current becomes 10 times. What is n ?
(i) Derive an expression for drift velocity of free electrons.
(ii) How does drift velocity of electrons in a metallic conductor vary with increase in temperature ? Explain.