Chapter 28: Answers to Stop to Think Questions and Odd-Numbered Exercises and Problems

Stop to Think Questions

1. a, b, and d. These three are the same circuit because the logic of the connections is the same. In c, the functioning of the circuit is changed by the extra wire connecting the two sides of the capacitor.
2. $Δ V$ increases by 2 V in the direction of I. Kirchhoff’s loop law, starting on the left side of the battery, is then $+ 12 V + 2 V - 8 V - 6 V = 0$ .
3. $P_{B} > P_{D} > P_{A} > P_{C}$ . The power dissipated by a resistor is $P_{R} = (Δ V_{R})^{2} / R$ . Increasing R decreases $P_{R};$ increasing $Δ V$ increases $P_{R}$ . But the potential has a larger effect because $P_{R}$ depends on the square of $Δ V_{R}$ .
4. $I = 2 A f o r a l l . V_{1} = 20 V, V_{2} = 16 V, V_{3} = 10 V, V_{4} = 8 V, V_{5} = 0 V$ . The potential is 0 V on the right and increases by IR for each resistor going to the left.
5. $A > B > C = D .$ All the current from the battery goes through A, so it is brightest. The current divides at the junction, but not equally. Because B is in parallel with $C + D$ but has half the resistance, twice as much current travels through B as through $C + D$ . So B is dimmer than A but brighter than C and D. C and D are equal because current is the same through bulbs in series.
6. b. The two $2 Ω$ resistors are in series and equivalent to a $4 Ω$ resistor. Thus $τ = R C = 4 s$ .