The current, in the LCR circuit shown in the figure is observed to lead the voltage in phase. Without making any other change in the circuit, a capacitor,of capacitance C₀, is (appropriately) joined to the capacitor C. This results in making the current,in the ‘modified’ circuit, flow in phase with theapplied voltage.
Draw a diagram of the ‘modified’ circuit and obtain an expression for C₀ in terms of ω, L and C.
Draw a diagram of the ‘modified’ circuit and obtain an expression for C₀ in terms of ω, L and C.
In the following circuit, calculate (i) the capacitance of the capacitor, if the power factor of the circuit is unity, (ii) the Q-factor of this circuit. What is the significance of the Q-factor in ac circuit ? Given the angular frequency of the ac source to be 100rad/s. Calculate the average power dissipated in the circuit.
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.
(i) Find the value of the phase difference between the current and the voltage in the series LCR circuit shown below. Which one leads in phase : current or voltage ?
(ii) Without making any other change, find the value of the additional capacitor C₁, to be connected in parallel with the capacitor C, in order to make the power factor of the circuit unity.
An alternating voltage E = E₀ sin ωt is applied to the circuit containing a resistor R connected in series with a black box. The current in the circuit is found to be I=I₀ (sin ωt+π/4)
A sinusoidal voltage of peak value 10 V is applied to a series LCR circuit in which resistance,capacitance and inductance have values of 10 Ω,1 µF and 1 H respectively. Find
(i) the peak voltage across the inductor at resonance
(ii) quality factor of the circuit.
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.
An inductor of 200 mH, capacitor of 400 µF and a resistor of 10 Ω are connected in series to ac source of 50 V of variable frequency. Calculate the
(a) angular frequency at which maximum power dissipation occurs in the circuit and the corresponding value of the effective current, and
(b) value of Q-factor in the circuit.
A charge + Q, is uniformly distributed within a sphere of radius R. Find the electric field, due to this charge distribution, at a distant point r from the centre of the sphere where :
(i) 0 < r < R
(ii) r > R
(i) Deduce the relation between current I flowing through a conductor and drift velocity of the electrons.
(ii) Figure shows a plot of current ‘I’ flowing through the cross-section of a wire versus the time ‘t’. Use the plot to find the charge flowing in 10 s through the wire.
(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.
Two thin concentric and coplanar spherical shells, of radii a and b (b > a) carry charges, q and Q, respectively. Find the magnitude of the electric field, at a point at distance x, from their common centre for :
(i) 0 < x < a
(ii) a x < b
(iii) b x <
(i) When an ac source is connected to an ideal capacitor show that the average power supplied by the source over a complete cycle is zero.
(ii) A lamp is connected in series with a capacitor.Predict your observation when the system is connected first across a dc and then an ac source.What happens in each case if the capacitance of the capacitor is reduced ?
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).
An inductor of 200 mH, capacitor of 400 µF and a resistor of 10 Ω are connected in series to ac source of 50 V of variable frequency. Calculate the
(a) angular frequency at which maximum power dissipation occurs in the circuit and the corresponding value of the effective current, and
(b) value of Q-factor in the circuit.