Chapter 27: Circuits

Figure 27-79 shows three$\mathbf{20}\mathbf{.0}\mathbf{}\mathbf{\text{\hspace{0.17em}Ω}}$resistors. Find the equivalent resistance between points (a), (b), and (c). (Hint: Imagine that a battery is connected between a given pair of points.)

A 120V power line is protected by a 15A fuse. What is the maximum number of 500W lamps that can be simultaneously operated in parallel on this line without “blowing” the fuse because of an excess of current?

Figure 27-63 shows an ideal battery of emf e= 12V, a resistor of resistance$\mathbf{R}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\Omega }$,and an uncharged capacitor of capacitance $\mathbf{C}\mathbf{=}\mathbf{4}\mathbf{.}\mathbf{0}\mathbf{\mu F}$ . After switch S is closed, what is the current through the resistor when the charge on the capacitor $\mathbf{8}\mathbf{.}\mathbf{0}\mathbf{\mu C}$?

A group of Nidentical batteries of emfand internal resistance rmay be connected all in series (Fig. 27-80a) or all in parallel (Fig. 27-80b) and then across a resistor R. Show that both arrangements give the same current in Rif R=r.

In Fig. 27-48,${\mathit{R}}_{\mathbf{1}}\mathbf{=}{\mathit{R}}_{\mathbf{2}}\mathbf{=}\mathbf{10}\mathit{\Omega }$, and the ideal battery has emf.$\mathit{\epsilon }\mathbf{=}\mathbf{12}\mathbf{}\mathbf{\text{V}}$

(a) What value of${\mathbf{\text{R}}}_{\mathbf{3}}$maximizes the rate at which the battery supplies energy and (b) what is that maximum rate?

In Fig 27-66, the ideal battery has emf30 V, the resistances are${\mathit{R}}_{\mathbf{1}}\mathbf{=}$20 kΩ,and${\mathit{R}}_{\mathbf{2}}\mathbf{=}$10 kΩ, and the capacitor is uncharged. When the switch is closed at time t= 0, what is the current in

(a) Resistance 1 and

(b) Resistance 2?

(c) A long time later, what is the current in resistance 2?

(a) In electron-volts, how much work does an ideal battery with a 12.0 V emf do on an electron that passes through the battery from the positive to the negative terminal? (b) If 3.40$\mathbf{\times }{\mathbf{10}}^{\mathbf{18}}$electrons pass through each second, what is the power of the battery in watts?

Two resistors are wired to a battery.

(a) In which arrangement, parallel or series, are the potential differences across each resistor and across the equivalent resistance all equal?

(b) In which arrangement are the currents through each resistor and through the equivalent resistance all equal?