Solutions - Midterm 2

PHY1020U MIDTERM I March 15, 2006 830 930 am Instructor Franco Gaspari Instructions Calculators and personal formula sheet allowed. No other aids. For full marks you must show methods, compute numerical results when requested and state units. You can write your answers also on the back of the pages. DO NOT UNSTAPLE THIS PAGE. Part I /20 Problem I /10 Problem II /20 Final Mark /50 SHAPE MERGEFORMAT a) EMBED Equation.3 1 in the first case, the length corresponds to L0.3 m, and the area is WxH(0.05x0.05)m2 therefore EMBED Equation.3 2 b) in the second case, the length corresponds to H0.05, and the area is LxW(0.3x0.05)m2 therefore EMBED Equation.3 2 Q2. Two capacitors C1 and C2 have both area A 0.01 m2 and separation d 0.02 mm. Capacitor C1 is filled with a dielectric (dielectric constant k 3.4). Find the equivalent capacitance if the two capacitors are in series. (5 marks) SHAPE MERGEFORMAT EMBED Equation.3 1 EMBED Equation.3 2 EMBED Equation.3 2Q3. The circuit below uses has the following components that is EMBED Equation.3 3Problem 1 total mark 10/10 Consider the circuit below. SHAPE MERGEFORMAT Calculate the equivalent capacitance Ceq (show all the steps). (5 marks) a) EMBED Equation.3 2 EMBED Equation.3 3 What is the potential difference across C4 (5 marks) b) EMBED Equation.3 2 EMBED Equation.3 3 Problem 2 total mark 20/20 Using Kirchhoff laws, calculate the steady state currents through each resistor after the switch is closed (indicate directions too) (15 marks). With the switch open, the current will flow only through the right loop and through resistors R2 and R3, which are in series 2 Then EMBED Equation.3 3 Select arbitrary direction of the currents (red arrows) and label nodes. 4 At node c we can see that, according to our labeling, we get EMBED Equation.3 also, from loop abcd EMBED Equation.3 , and from loop cefd 6 EMBED Equation.3 Some algebra gives EMBED Equation.3 5 Rough WorkFormula sheet Midterm 2 EMBED Equation.3 Capacitance EMBED Equation.3 Parallel Plate Capacitor EMBED Equation.3 Cylindrical Capacitor EMBED Equation.3 Spherical Capacitor EMBED Equation.3 Capacitor with dielectric EMBED Equation.3 Dielectric constant EMBED Equation.3 Capacitors in series EMBED Equation.3 Capacitors in parallel EMBED Equation.3 , EMBED Equation.3 Energy stored in a capacitor EMBED Equation.3 , EMBED Equation.3 Resistance formulas EMBED Equation.3 Power dissipated in a resistor EMBED Equation.3 Resistors in parallel EMBED Equation.3 Resistors in series EMBED Equation.3 Charging equation for current (RC circuit) EMBED Equation.3 Discharging equation for charge (RC circuit) EMBED Equation.3 Discharging equation for current (RC circuit)INCLUDEPICTURE ../../../My20Documents/Google20Talk20Received20Files/Chapter2028/PSE2803.eps MERGEFORMAT H0.05 m. L0.3 m. W0.05 m C2 C1 eoQFzyQSR@8xm v5zCw4QpJtLs4IQn-9Qmz2,_7LZAb//Jyem6DC, hEmmj3u/8yKDViQIFApwpU6923OeaOM._ Av5AO3Sx3MSW@sp 1/Yood9xw7Y7RoCzoyGNWzI z5VlrHEL- qz 0JeS45xUurBp)nJ9r29JeUU,7B73V59vj1DsrUc/vaVu 8Oj@rl-7/7 G.7d 0WJONs.TEVdPM24-OEYhB.gZnsCh nfeQV o-s)ahc(x2U-ZIyLicgw,IGcW16jhf5,aD0Pm@