<< Chapter < Page | Chapter >> Page > |
The material in this section is correct in theory. We should be able to verify it by making measurements of current and voltage. In fact, some of the devices used to make such measurements are straightforward applications of the principles covered so far and are explored in the next modules. As we shall see, a very basic, even profound, fact results—making a measurement alters the quantity being measured.
Can Kirchhoff’s rules be applied to simple series and parallel circuits or are they restricted for use in more complicated circuits that are not combinations of series and parallel?
Kirchhoff's rules can be applied to any circuit since they are applications to circuits of two conservation laws. Conservation laws are the most broadly applicable principles in physics. It is usually mathematically simpler to use the rules for series and parallel in simpler circuits so we emphasize Kirchhoff’s rules for use in more complicated situations. But the rules for series and parallel can be derived from Kirchhoff’s rules. Moreover, Kirchhoff’s rules can be expanded to devices other than resistors and emfs, such as capacitors, and are one of the basic analysis devices in circuit analysis.
Can all of the currents going into the junction in [link] be positive? Explain.
Apply the junction rule to junction b in [link] . Is any new information gained by applying the junction rule at e? (In the figure, each emf is represented by script E.)
(a) What is the potential difference going from point a to point b in [link] ? (b) What is the potential difference going from c to b? (c) From e to g? (d) From e to d?
Apply the loop rule to loop afedcba in [link] .
Apply the loop rule to loops abgefa and cbgedc in [link] .
Apply the loop rule to loop abcdefgha in [link] .
Apply the loop rule to loop aedcba in [link] .
Verify the second equation in [link] by substituting the values found for the currents ${I}_{1}$ and ${I}_{2}$ .
Verify the third equation in [link] by substituting the values found for the currents ${I}_{1}$ and ${I}_{3}$ .
Apply the junction rule at point a in [link] .
Apply the loop rule to loop abcdefghija in [link] .
Apply the loop rule to loop akledcba in [link] .
Find the currents flowing in the circuit in [link] . Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors .
Solve [link] , but use loop abcdefgha instead of loop akledcba. Explicitly show how you follow the steps in the Problem-Solving Strategies for Series and Parallel Resistors .
(a) ${\text{I}}_{1}=\text{4.75 A}$
(b) ${\text{I}}_{\text{2}}=-3\text{.}\text{5 A}$ $$
(c) ${\text{I}}_{3}=8\text{.}\text{25 A}$
Find the currents flowing in the circuit in [link] .
Unreasonable Results
Consider the circuit in [link] , and suppose that the emfs are unknown and the currents are given to be ${I}_{1}=5\text{.}\text{00 A}$ , ${I}_{2}=3\text{.0 A}$ , and ${I}_{3}=\mathrm{\u20132}\text{.}\text{00 A}$ . (a) Could you find the emfs? (b) What is wrong with the assumptions?
(a) No, you would get inconsistent equations to solve.
(b) ${I}_{1}\ne {I}_{2}+{I}_{3}$ . The assumed currents violate the junction rule.
Notification Switch
Would you like to follow the 'College physics' conversation and receive update notifications?