TEST Giving or receiving aid in any examination is cause for dismissal from the university. Perform the necessary calculation in the spaces provided. If additional space is required, use the backs of the questions sheets. ll work must be shown in order to receive FULL credit. Work must be legible and comprehensible, and answers should be clearly indicated.. parallel plate capacitor is constructed by filling the space between two square plates with blocks of three dielectric materials, as shown in figure below. You may assume the space that l>> d. (a) κ = ; d κ = ; d 3 κκ 3 = = d κ κ 3 3 3 3 κ 3 = d κ κκ 3 3 d κ κ 3 FIG. = = a) Find expression for a capacitance of the device in terms of the area and d, k and k and k 3. b) alculate the capacitance using the values =. cm, d=. mm, k =4.9, k =5.6 and k 3 =. Using the given values one can find: total =.76 F=.76 pf.. Find the equivalent capacitance between points a and b in the combination of capacitors shown in figure below
P 6. 9 s p = =.9 μf 5. 7. =.9 4. 6. =.9 μf FIG. 3. onsider the circuit shown in figure below, = 6. µf and = 3. µf and V=. V. apacitor is first charged by closing switch S. Switch S is then opened and the charged capacitor is connected to the uncharged capacitor = 3. µf by the closing the switch S. a) alculate the initial charge on = 6. µf b) alculate the final charge on = 3. µf c) alculate the final charge on = 6. µf and V = 6 = so Δ μ 6. =. and = μ Δ V = : = = 6. 3. or ( 3.) ( ) = ( 6.) 36 = = 9. = μ 4. μ = 8. μ 4. μ FIG. 3 4. onsider a series R circuit, shown in figure below, for which R=.MΩ, = 5. µf and ε=3. V.
Find a) The time constant of the circuit b) The maximum charge on a capacitor after the switch is closed c) Find the current in resistor s after the switch was closed 6 6 (a) R ( )( ) =. Ω 5. F = 5. s 6 (b) ( )( ) = ε = 5. 3. V = 5 μ ε tr 3.. (c) It () = e = exp = 4.6 μ 6 R. 6 6 (. )( 5. ) FIG. 4 5. What is escape speed of an electron launched from the surface of a. cm diameter plastic sphere that has been charged to n Energy is conserved. The electron ends up so far away from the plastic sphere that we can consider its potential energy to be zero. The charge of the plastic sphere must be positive. The minimum speed to escape is the speed that allows the electron to reach r f = when v f = m/s. The conservation of energy equation K f U f = K i U i is q J J = mvi qvi J = mvi ( e) 4πε R 9 ( ) ( ) 9 e q.6 9 7 vi = = 9. N m / 7.95 m/s 3 = m 4πε R 9. kg.5 m 6. The four identical. g spheres with charge q=x -9 are released simultaneously from rest at the vertices of a square of side L = cm and allowed to move away from each other. a) How fast is each particle moving when their distance from the center is doubled?
Each charge moves off on its diagonal line. ll charges have equal speeds. ( K U ) = ( K U ) i e e e e 4kq kq 4kq kq = 4 mv L L L L e kq = mv L f v = e kq 8 ml b) What is the speed of each sphere when they are very far apart? The total potential energy of the four spheres before they are allowed to move is U i = (U U 3 U 34 U 4 ) (U 3 U 4 ) ll the charges are identical, r = r 3 = r 34 = r 4 = L = cm, and r 3 = r 4 = cm. The initial potential energy is ( 9 )( 9 ) ( 9 )( 9 ) U i = = 5 4 48.73 J 4πε. m 4πε.44 m Since all charges are at rest, K i = J. s the spheres are allowed to move away from one another and they are far apart, U f = J. The final kinetic energy is ( ) ( ) K = 4 mv =. kg v 3 f f f From the energy conservation equation U f K f = U i K i, ( ). kg v = 48.73 J v f =.494 m/s 3 5 f 7. If the current carried by conductor is doubled, what happens to the (a) harge carrier density? n is unaffected (b) urrent density? I J= I So current doubles. (c) Electron drift velocity? J= nev d So v d also doubles.
mσ (d) The average time interval between the collisions? τ = is unchanged as long as σ does not change due to a temperature change in the conductor.. harge of uniform density (3.5 n/m) is distributed along the circular arc shown. Determine the electric potential (relative to zero at infinity) at point P. nq a. 6 V b. 4 V c. 5 V d. 33 V e. V R R 6 P d. The circuit below contains three watt light bulbs. The emf E = V. Which light bulb(s) is(are) the brightest? E a. b. c. d. and e. ll three are equally bright. a.
3. The circuit below contains 5 light bulbs. The emf is V. Which light bulb(s) is(are) brightest? V E D a. : The one closest to the positive terminal of the battery. b. and : The bulbs closest to the positive terminal of the battery. c. and : ecause they are closest to the terminals of the battery. d. and D: ecause they receive current from and and from E. e. E: ecause the potential difference across E is that of the battery. e. 4. If I =. in the circuit segment shown below, what is the potential difference V V? I V Ω V a. V b. V c. V d. V e. 3 V b. 5. t what rate is thermal energy generated in the 3-Ω resistor? Ω 3 V 3 Ω 5. Ω 5. Ω a. W b. 7 W c. 6 W d. 3 W e. 3 W d.
6. Which of the following represents the equipotential lines of a dipole? e. (a) (b) (c) (d) (e) 7. If a = 3 cm, b = cm, q =. n, and = 3. n in the figure, what is the potential difference, V V? a a b a q a. 6 V b. 7 V c. 84 V d. 96 V e. 48 V 8. Extra: Determine the equivalent capacitance of the combination shown in figure below. (Suggestion: consider the symmetry involved) a. 5 b. 6 c. 4 3 d. 3 4 e. c.