8.02X Electricity and Magnetism

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a) What is the output voltage V outof the op-amp in terms of the input voltage V into pin3, and the voltage at pin 2, V 2, and the amplification A? (Note: all voltages are withrespect to common).b) Derive an expression for the voltage at pin 2, in terms of R 1and R 2.c) Derive an expression for the closed loop gain G = V outV inin terms of R 1, R 2, and A.d) Calculate the value of the gain G, clearly indicating any approximations you havemade.Problem 3: CalibrationThe calibration circuit for the amplifier is shown in the figure below. When the multimeteris set on the 250 mV scale the multi-meter has a resistance of 5k .a) When the 5k pot is turned 2/3 of the way in the direction of the +6V line from the6V end, what is the voltage difference between common C and the 5k pot slider?b) When the 5k pot is set as in part a), calculate the voltage difference between thecommon C and point D which is connected via a clip lead to the input A?c) What output voltage did you read when your pot was set as in part a) while you werecalibrating your amplifier?
MIT Department of PhysicsPhysics 8.02X Spring 2005Solution to Problem Set #9Problem 1 (20 points) The 1200 dipole magnets of the LHC accelerator atCERN will have a field of 8 Tesla. Approximate the magnet as two square loopsof dimension 14m x 0.3 m, with a distance of 10cm between the two loops(similar to the arrangement in question 4 of quiz 3).(a) What direction should the field have to keep protons going clockwise on acircular trajectory?Magnet:End view:B14m 0.3my0.1m0.1mx0.3mAt the center, the four fields add up to for a net vertical field.The accelerator, made by 1200 dipole magnets, is as the following:BBBvprotonFmagnets F = qv×B. The direction of B is shown in figure above.(b) What is the current in each loop needed to create a field of 8T in the midplaneof the two loops?1
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8.02X Electricity and Magnetism

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