Kirchoff's Laws. A circuit contains 3 known resistors, 2 known batteries, and 3 unknown currents as shown. Assume the current flows through the circuit as shown (this is our initial guess, the actual currents may be reverse). Use the sign convention that a potential drop is negative and a potential gain is positive. E₂ = 8V R₁₁ = 50 R₂ = 80 b с w 11 www 12 13 E₁ = 6V R3 = 20 a) Apply Kirchoff's Loop Rule around loop abefa in the clockwise direction starting at point a. (2 pt). b) Apply Kirchoff's Loop Rule around loop bcdeb in the clockwise direction starting at point b. (2 pt). c) Apply Kirchoff's Junction Rule at junction b (1 pt). d) Solve the above 3 equations for the unknown currents I1, 12, and 13 and specify the direction of the current around each loop. (5 pts) I1 = A 12 = A 13 = A Direction of current around loop abef Direction of current around loop bcde (CW or CCW) (CW or CCW)

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4.) The diagram shows the electric field lines of a positively charged conducting sphere of radius R and charge Q. A B Points A and B are located on the same field line. A proton is placed at A and released from rest. The magnitude of the work done by the electric field in moving the proton from A to B is 1.7×10-16 J. Point A is at a distance of 5.0×10-2m from the centre of the sphere. Point B is at a distance of 1.0×10-1 m from the centre of the sphere. (a) Explain why the electric potential decreases from A to B. [2] (b) Draw, on the axes, the variation of electric potential V with distance r from the centre of the sphere. R [2] (c(i)) Calculate the electric potential difference between points A and B. [1] (c(ii)) Determine the charge Q of the sphere. [2] (d) The concept of potential is also used in the context of gravitational fields. Suggest why scientists developed a common terminology to describe different types of fields. [1]