- Consider the circuit with batteries, resistors, and currents as drawn below. Throughout this problem be careful of +/- signs.
(a) Write Kirchoff’s Junction Rule for the junction of
wires.
(b) Using the currents as drawn in the circuit to the
right, write Kirchoff’s Loop Rule for the counterclockwise
loop around the upper half of this circuit (see figure below).
(c) Using the currents as drawn in the circuit to the
right, write Kirchoff’s Loop Rule for the clockwise loop
around the lower half of this circuit (see figure below).
part (b) part (c)
(d) Find the unknown currents (i1, i2, and i3) in the circuit.
- Begin with the equation you found in step (b). Solve for i1.
In other words isolate i1. After you do this you will have an equation that looks like i1 = [stuff that includes i2].
- Now take the equation you found in step (c) are solve for i3.
In other words isolate i3. After you do this you will have an equation that looks like i3 = [stuff that includes i2].
iii. Plug the equations from steps i. and ii. into Kirchoff’s Junction Rule (that you found in step (a) of this problem).
- Now you have a single equation that only depends on i2. Solve for i2.
- Plug the value of i2 that you found into the equations in steps i. and ii. to find i1 and i3.
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