**P. 4269.** 4 kJ heat is added to a sample of gas whose original temperature is 300 K. Both the volume and the pressure of the gas is doubled, and the gas does 1 kJ work on its environment during the process. The graph of the process on the *p*-*V* diagram is a straight line.

*a*) How many moles of gas are there in the sample?

*b*) How many atoms constitute one molecule of the gas?

(4 points)

**P. 4270.** The switch in the circuit, shown *in the figure* has been closed for quite a long time. (*U*=100 V, *C*=2 F, *R*_{1}=20 , *R*_{2}=30 , *R*_{3}=12 .)

*a*) Determine the charge on the capacitor.

*b*) The switch is opened. What amount of charge flows through the resistor *R*_{1} after opening the switch?

*c*) How much work is done on the resistor *R*_{1} after opening the switch?

(4 points)

**P. 4271.** There is a pair of parallel, horizontal, conducting rails in uniform vertically downward magnetic field of induction *B*=0.5 T. The two rails are at a distance of =10 cm and they are connected to a rechargeable battery of potential difference *U*_{0}=12 V. A metal rod of mass *m*=50 g, and of resistance *R*=2 , is placed onto the rails, perpendicularly to them. The coefficient of friction between the rod and the rails is =0.3.

*a*) What is the initial acceleration of the rod when switch K is closed?

*b*) What would the final speed of the rod be if the rails are very long?

*c*) Estimate, (try to give a precise estimation) the covered distance, and the time during which the speed of the rod increases from to .

(5 points)

**P. 4272.** We have 4 alike, ideal diodes in order to rectify the sinusoidal voltage of the mains. The r.m.s. value of the mains is 230 V, and its frequency is 50 Hz. (Any number of diodes can be used up to 4.)

*a*) What circuit would you build in order to make a half-wave rectifier?

*b*) What circuit would you build in order to make a full-wave rectifier?

*c*) Determine the r.m.s. value of the voltage in both cases.

(4 points)

**P. 4273.** Two unknown impedances are connected in parallel to the mains, of voltage 230 V and of frequency 50 Hz. The maximum value of the current in the main branch is 20 A. The current through one of the impedances leads the current in the main branch by an angle of , and through the other impedance the current lags behind the current in the main branch by an angle of .

*a*) What are the instantaneous current values in the two branches at *t*=0.01 s, if the current in the main branch is zero at *t*=0?

*b*) What are the values of the inductance and the capacitance in the two branches?

(5 points)