How does the sign of the phase angle `phi`,by the supply voltage leads the current in an LCR series circuit,change as the supply frequency is gradually increased from very low to very high values?

In a circuit L,Cand R are connected in series with an alternating voltage of frequency f the current leads the voltage by 45^@. The value of C is

Read the following paragraph and answer the questions given below it: The resistance of a metal falls when cooled below room temperature. Many scientists believed that the value of the resistance would become constant at some very low temperature, allowing the current to flow with little or no resistance. H. K. Onnes successfully liquefied helium in 1908 by cooling it to about 4 K. In 1911, while investigating the electrical property of very pure mercury. Onnes discovered that at a temperature of 4.2 kelvin, its resistance practically vanished. This new state, on account of its extraordinary property, is now called the superconducting state and the phenomenon is called superconductivity. A superconductor, below a certain critical temperature, offers almost zero resistance to a flow of current through it. Onnes also discovered that a superconductor exhibits persistent current: once set up, the current continues to flow for a very long time without an electric potential difference driving it and without significant loss. Superconductivity is used in many diverse areas, such as magnetically levitated trains, transmission of electricity, increasing speed of computers, in MRI (magnetic resonance imaging). At what temperature does the resistance of very pure mercury become almost zero?

Figure shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Omega maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02V (for very moderate currents upto a few mA) gives a balance point at 67.3 cm length of the wire.To ensure that very low current drawn from the standard cell,a very high resistance of 600 k Omega is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf E and the balance point found similarly,turns out to be at 82.3 cm length of the wire . Would the circuit work well for determining an extremely small emf, say of the order of a few m V (such as the typical emf of a thermo-couple) ? If not , how will you modify the circuit ?

Figure shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Omega maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02V (for very moderate currents upto a few mA) gives a balance point at 67.3 cm length of the wire.To ensure that very low current drawn from the standard cell,a very high resistance of 600 k Omega is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf E and the balance point found similarly,turns out to be at 82.3 cm length of the wire . What purpose does the high resistance of 600 k Omega have?

Figure shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Omega maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02V (for very moderate currents upto a few mA) gives a balance point at 67.3 cm length of the wire.To ensure that very low current drawn from the standard cell,a very high resistance of 600 k Omega is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf E and the balance point found similarly,turns out to be at 82.3 cm length of the wire . What is the value of E ?

Figure shows a potentiometer with a cell of 2.0 V and internal resistance 0.40 Omega maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of 1.02V (for very moderate currents upto a few mA) gives a balance point at 67.3 cm length of the wire.To ensure that very low current drawn from the standard cell,a very high resistance of 600 k Omega is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf E and the balance point found similarly,turns out to be at 82.3 cm length of the wire . Is the balance point affected by the internal resistance of the driver cell ?

A coil having an inductance of 1/pi henry is connected in series with a resistance of 300Ω. if 20 volt from a 200 cycle source are impressed across the combination, the value of the phase angle between the voltage and the current is :

An electrical device draws 2 kW power from AC mains (voltage 223 V (rms) = sqrt50,000 V ). The current differs (lags) in phase by phi (tan phi = (-3)/4) as compared to voltage . Find i) R, ii) X_C-X_L , and iii) I_M . Another device has twice the values for R, X_C and X_L .How is the answer affected ?

A sinusoidal voltage of peak value 283V and frequency 50 Hz is applied to a series LCR circuit in which R = 3 Omega , L = 25.48 mH and C = 796 muf . Find:-The phase difference between the voltage across source and the currents