Learning Goal: To understand the origins of both of Kirchhoff\'s rules and how t

Question

Learning Goal:

To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem.

This problem introduces Kirchhoff's two rules for circuits:

Kirchhoff's loop rule: The sum of the voltage changes across the circuit elements forming any closed loop is zero.

Kirchhoff's junction rule: The algebraic sum of the currents into (or out of) any junction in the circuit is zero.

The figure (Figure 1) shows a circuit that illustrates the concept of loops, which are colored red and labeled loop 1 and loop 2. Loop 1 is the loop around the entire circuit, whereas loop 2 is the smaller loop on the right. To apply the loop rule you would add the voltage changes of all circuit elements around the chosen loop. The figure contains two junctions (where three or more wires meet)--they are at the ends of the resistor labeled R3. The battery supplies a constant voltage Vb, and the resistors are labeled with their resistances. The ammeters are ideal meters that read I1 and I2 respectively.

The direction of each loop and the direction of each current arrow that you draw on your own circuits are arbitrary. Just assign voltage drops consistently and sum both voltage drops and currents algebraically and you will get correct equations. If the actual current is in the opposite direction from your current arrow, your answer for that current will be negative. The direction of any loop is even less imporant: The equation obtained from a counterclockwise loop is the same as that from a clockwise loop except for a negative sign in front of every term (i.e., an inconsequential change in overall sign of the equation because it equals zero).

Part A

The junction rule describes the conservation of which quantity? Note that this rule applies only to circuits that are in a steady state.

A.current
B.voltage
C.resistance

Part B

Apply the junction rule to the junction labeled with the number 1 (at the bottom of the resistor of resistance R2).

Answer in terms of given quantities, together with the meter readings I1 and I2 and the current I3.

Part C

Apply the loop rule to loop 2 (the smaller loop on the right). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow. Remember that the current meter is ideal.

Express the voltage drops in terms of Vb, I2, I3, the given resistances, and any other given quantities.

Part D

Now apply the loop rule to loop 1 (the larger loop spanning the entire circuit). Sum the voltage changes across each circuit element around this loop going in the direction of the arrow.

Express the voltage drops in terms of Vb, I1, I3, the given resistances, and any other given quantities.

Explanation / Answer

A)
Junction rule describes the conservation of current.

B)
Currents that are entering at the junction 1 = I2 + I3
Currents that are leaving the junction 1 = I1
According to junction rule, I1 = I2 + I3
I1 - I2 - I3 = 0

C)
Applying Kirchhoff's loop rule to loop 2
I3 R3 - I2 R2 = 0

D)
Applying Kirchhoff's loop rule to loop 1,
Vb = I1 R1 + I3 R3
Vb - I1 R1 - I3 R3 = 0

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.