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Junction Rule: sum of current entering junction equals sum of current leaving junction. Loop Rule: the sum of potential differences around a close loop equals zero. Problem-Solving Strategy: Using Kirchhoff ’s Rules to Analyze a Circuit 1. Replace any series or parallel combinations with their equivalents. 2. Assign variables to the currents in each branch of the circuit(I1,I2,...)and choose directions for each current. Draw the circ uit with the current directions indicated by arrows. It does not matter whether or not you choose the correct direction. 3. Apply Kirchhoff’s junction rule to all but one of the junctions in the circuit. (Applying it to every junction produces one redundant equation.) Remember that current into a junction is positive; current out of a junction is negative. 4. Apply Kirchhoff’s loop rule to enough loops so that, together with the junction equations, you have the same number of equations as unknown quantities. For each loop, choose a starting point and a direction to go around the loop. Be care- ful with signs. For a resistor, if your path through a resistor goes with the current (“downstream”), there is a potential drop; if your path goes against the current (“upstream”), the potential rises. For an emf, the potential drops or rises depend- ing on whether you move from the positive terminal to the negative or vice versa; the direction of the current is irrelevant. A helpful method is to write “+” and “–” signs on the ends of each resistor and emf to indicate which end is at the higher potential and which is at the lower potential. 5. Solve the loop and junction equations simultaneously. If a current comes out negative, the direction of the current is opposite to the direction you chose. 6. Checkyourresultusingoneormoreloopsorjunctions.Agoodchoiceisaloop that you did not use in the solution.