Coco Physics Homework-230819
NO. 1
A sinusoidal alternating voltage supply is connected to a bridge rectifier consisting of
four ideal diodes. The output of the rectifier is connected to a resistor R and a
capacitor C as shown in Fig. 6.1.
The function of C is to provide some smoothing to the potential difference across R.
The variation with time t of the potential difference V across the resistor R is shown in
Fig. 6.2.
a. Use Fig. 6.2 to determine, for the alternating supply,
i. the peak voltage,
peak voltage = ............................................. V [1]
ii. the root-mean-square (r.m.s.) voltage,
r.m.s. voltage = ............................................. V [1]
iii. the frequency. Show your working.
frequency = ........................................... Hz [2]
b. The capacitor C has capacitance 5.0 μF.
For a single discharge of the capacitor through the resistor R, use Fig. 6.2 to
i. determine the change in potential difference,
change = ............................................. V [1]
ii. determine the change in charge on each plate of the capacitor,
change = ............................................ C [2]
iii. show that the average current in the resistor is 1.1 × 10–3 A. [2]
c. Use Fig. 6.2 and the value of the current given in (b)(iii) to estimate the resistance
of resistor R.
resistance = ............................................. Ω [2]
NO. 2
A capacitor consists of two metal plates separated by an insulator, as shown in Fig.
3.1.
The potential difference between the plates is V. The variation with V of the magnitude
of the charge Q on one plate is shown in Fig. 3.2.
a. Explain why the capacitor stores energy but not charge.
............................................................................... [3]
b. Use Fig.3.2 (next page) to determine
i. the capacitance of the capacitor,
capacitance = .......................................... μF [2]
ii. the loss in energy stored in the capacitor when the potential difference V is
reduced from 10.0 V to 7.5 V.
energy = ......................................... mJ [2]
c. Three capacitors X, Y and Z, each of capacitance 10 μF, are connected as shown
in Fig. 3.3.
Initially, the capacitors are uncharged.
A potential difference of 12 V is applied between points A and B.
Determine the magnitude of the charge on one plate of capacitor X.
charge = ......................................... μC [3]
NO. 3
a. Two horizontal metal plates are connected to a power supply, as shown in Fig. 7.1.
The separation of the plates is 40 mm.
The switch S is then closed so that a potential difference of 1.2kV is applied
across the plates.
i. On Fig. 7.1, draw six field lines to represent the electric field between the
metal plates. [2]
ii. Calculate the electric field strength E between the plates.
E = ...................................... V m–1 [2]
b. The switch S is opened and the plates lose their charge. Two very small metal
spheres A and B joined by an insulating rod are placed between the metal plates
as shown in Fig. 7.2.
Sphere A has charge –e and sphere B has charge +e, where e is the charge of a
proton.
The length AB is 15mm. The rod is supported at its centre C so that the rod is
horizontal and in equilibrium.
The switch S is then closed so that the potential difference of 1.2kV is applied
across the plates.
i. There is a force acting on A due to the electric field between the plates.
Show that this force is 4.8 × 10–15N. [2]
ii. The insulating rod joining A and B is fixed in the position shown in Fig. 7.2.
Calculate the torque of the couple acting on the rod.
torque = ........................ unit .................. [3]
iii. The insulating rod is now released so that it is free to rotate about C.
State and explain the position of the rod when it comes to rest.
.................................................................... [2]
NO. 4
a. State what is meant by an electric field.
........................................................................................... [1]
b. The electric field between an earthed metal plate and two charged metal spheres
is illustrated in Fig.5.1.
i. On Fig.5.1, label each sphere with (+) or (–) to show its charge. [1]
ii. On Fig.5.1, mark a region where the magnitude of the electric field is
constant (label this region C), [1]
decreasing (label this region D). [1]
c. A molecule has its centre P of positive charge situated a distance of 2.8 × 10–10 m
from its centre N of negative charge, as illustrated in Fig.5.2.
The molecule is situated in a uniform electric field of field strength 5.0 × 104 V m–1.
The axis NP of the molecule is at an angle of 30° to this uniform applied electric
field.
The magnitude of the charge at P and at N is 1.6 × 10–19 C.
i. On Fig. 5.2, draw an arrow at P and an arrow at N to show the directions of
the forces due to the applied electric field at each of these points. [1]
ii. Calculate the torque on the molecule produced by the forces in (i).
torque = ......................................... N m [2]
NO. 5
A planet of mass m is in a circular orbit of radius r about the Sun of mass M, as
illustrated in Fig. 1.1.
The magnitude of the angular velocity and the period of revolution of the planet about
the Sun are ω and T respectively.
a. State
i. what is meant by angular velocity,
....................................................................[2]
ii. the relation between ω and T.
....................................................................[2]
b. Show that, for a planet in a circular orbit of radius r, the period T of the orbit is
given by the expression
T2 = cr3
where c is a constant. Explain your working. [4]
c. Data for the planets Venus and Neptune are given in Fig. 1.2.
Assume that the orbits of both planets are circular.
i. Use the expression in (b) to calculate the value of T for Neptune.
T = ....................................... years [2]
ii. Determine the linear speed of Venus in its orbit.
speed = ..................................... km s–1 [2]
NO. 6
a. On the axes of Fig. 2.1, sketch the variation with distance from a point mass of the
gravitational field strength due to the mass. [2]
b. On the axes of Fig. 2.2, sketch the variation with speed of the magnitude of the
force on a charged particle moving at right-angles to a uniform magnetic field. [2]
c. On the axes of Fig. 2.3, sketch the variation with time of the power dissipated in a
resistor by a sinusoidal alternating current during two cycles of the current. [3]
NO. 7
A particle has mass m and charge +q and is travelling with speed v through a vacuum.
The initial direction of travel is parallel to the plane of two charged horizontal metal
plates, as shown in Fig. 6.1.
The uniform electric field between the plates has magnitude 2.8×104 V m–1 and is zero
outside the plates.
The particle passes between the plates and emerges beyond them, as illustrated in
Fig. 6.1.
a. Explain why the path of the particle in the electric field is not an arc of a circle.
.........................................................................[1]
b. A uniform magnetic field is now formed in the region between the metal plates.
The magnetic field strength is adjusted so that the positively charged particle
passes undeviated between the plates, as shown in Fig. 6.2.
i. State and explain the direction of the magnetic field.
....................................................................[2]
ii. The particle has speed 4.7×105 m s–1.
Calculate the magnitude of the magnetic flux density.
Explain your working.
magnetic flux density = .............................. T [3]
c. The particle in (b) has mass m, charge +q and speed v.
Without any further calculation, state the effect, if any, on the path of a particle
that has
i. mass m, charge –q and speed v,
.................................................................[1]
ii. mass m, charge +q and speed 2v,
.................................................................[1]
iii. mass 2m, charge +q and speed v.
.................................................................[1]