Capacitances of Capacitors - General Physics - Past Paper, Exams of Physics

Download Capacitances of Capacitors - General Physics - Past Paper and more Exams Physics in PDF only on Docsity! 20.07.2006 EP106 General Physics II Page 1/2 UNIVERSITY OF GAZIANTEP DEPARTMENT OF ENGINEERING PHYSICS EP 106 General Physics II First Midterm Exam SUMMER SCHOLL Date: 20/07/2006 Time: 100 min. Name Surname Dep. Signature -------- -------- ------ -------- • The steps of solution of each problem should be shown clearly in the space provided. • Write your answers in boxes provided, otherwise your answer will not be considered. • Useful constants:g = 9.8 m/s2 , k = 9x109 Nm2/C2, e = -1.602x10-19C, ε0= 8.85x10-12 C2/Nm2 Ques. Mark 1 2 3 4 5 xxxxx 6 xxxxx Total Out of 100 % QUESTION 1 (25 %) What is the charge density on the surface of a conducting sphere of radius 15 cm whose potential on the surface of the sphere is 200 V. 215 10 , 200 Q r m V Volts and V k R −= × = = on the sphere. Since 24Q Rσ π= × then 24 4 R V V k R k R σ π σ π =
= . Substituting values, we get 11 29.55 10 /C mσ = × QUESTION 2 (25 %) (a) When two capacitors are connected in parallel, the resulting combination has a total capacitance 9
F. When the same two capacitors are connected in series, the resulting combination has a total capacitance 2
F. What are the capacitances of the two capacitors? 1 29 PARALLEL eqC F C Cµ= = + and 1 2 1 2 2SERIESeq C C C F C C µ= = + , then 1 22 9 C C F F µ µ = and 21 2 18( )C C Fµ= so that 1 218 /C C= . Inserting C1 in A eqC , then one gets 1 2 2 2 18 9 9C C F C C µ+ = + = . Solving for C2, one finds that 2 23 6C F OR C Fµ µ= = . So that we write 2 1 3 6 6 3 C F or F C F or F µ µ µ µ = = (b) If these two capacitors are connected in parallel to a voltage source which has 12 Volts, what are the accumulated charges and voltage accross on each capacitor? For the PARALLEL case, it is known that the potential is same for all units in circuit. Then, 1 1 1 1 112*6 72q V C q q Cµ=
=
= and 2 2 1 112*3 36q V C q q Cµ=
=
= (c) Repeat part (b), if these two capacitors are connected in series. For the SERIES case, it is known that the charge on the C’s are the same. Then 1 2total EqQ q q VC= = = and 2EqC Fµ= for series. So 1 2 12*2 24totalQ q q Cµ= = = = . Finally, 11 1 24 4 6 q C V Volts C C µ µ = = = and 1 1 1 24 8 3 q C V Volts C C µ µ = = = . R