PHYS 222 Worksheet 12 – Kirchhoff's Laws - Iowa State University

PHYS 222Worksheet 12 – Kirchhoff’s LawsSupplemental InstructionIowa State UniversityLeader: Alek JerauldCourse: PHYS 222Instructor: Dr. Paula Herrera-SiklódyDate: 2/12/12Useful EquationsI 0Junction Rule. The algebraic sum of the currents into anyjunction is zero.V 0Loop Rule. The algebraic sum of the potential differenceDiagramsin any loop must equal zero.Related Problems

1) Find the following for the circuit (Book 26.21)(Dots on the circuit represent starting points for the loop method)(a) Current in resistor RUsing the junction rule at junction (a) :64I 0I2A(b) Resistance RUsing loop rule on loop (1) :2R 283(6) 0 R 5 (c) Unknown EMFUsing loop rule on loop (2) :6(4) 3(6) 042 V(d) If the circuit is broken at point x, what is the current in resistor R?Since the middle branch is broken, we can use the loop rule on loop (1) again, but solvingfor a new current:5 I' 283 I' 0I' 3.5A

2) Both meters are ideal. Voltmeter reads 16.0 V when switch is open. Find the EMF. Whatwill the ammeter read when the switch is closed? (Book 26.27)By junction rule at junction (a) :16I3 0.32 A50 I I 0.32 01 2Using loop rule on loop (1) :20I30(0.32) 50(0.32) 02Using loop rule on loop (2) :75I30(0.32) 50(0.32) 01Now there are three equations with three unknowns. Solve for each variable:I10.3413AI2 0.6613 A 28.82 VWhen switch is closed, using loop (3) the ammeter reads:2550 I3' 0I' 0.50A3

3) All meters are idealized and the batteries have no appreciable internal resistance. (Book26.29)(a) With the switch open, what is the reading of the voltmeter?Using loop (1) :25100I15 75I 0I0.2286AV V V 0.2286(75) 15 2.145 Vbaba(b) With the switch closed, what is the reading of the voltmeter?When the switch is close, the middle branch becomes a straight wire (short circuit),meaning the voltage across it is zero. Since the right branch is in parallel with the middlebranch, it too has a voltage of zero:V = 0 V(c) With the switch closed, find the reading of the ammeter. What is the direction of thecurrent?Using the junction rule at junction (a) : I1 I2 I ' 0Using loop (2) :25100I 01Using loop (1) again with a different current in the right branch:25100I1575 I' 01Now there are three equations with three unknowns. Solve for each variable:I1 0.25 AI' 0.2 AI 0.05 A2

4) Find the three currents I 1 , I 2 , I 3 . (Book 26.61)Using loop (1) :12 1I 5( I I ) 0Using loop (2) :2 2 31I 98 I I 01 1 3Using loop (3) :10I 91I 1I12 03 1 2Now there are three equations with three unknowns. Solve for each variable:III123 0.848 A 2.14 A 0.171 A