27. Resistors & DC Circuits

What is current and voltage across each resistor below?

What is the value of resistor R in FIGURE EX28.16?

Consider two unequal resistors, of resistance R₁ and R₂, that are connected either in series or in parallel. Fill in the Table below assuming the electric potential on the low-voltage end of the combination is V_A volts and the potential at the high-voltage end of the combination is V_B volts. First draw diagrams.

A 300 μF capacitor is charged to 9.0 V, then connected in parallel with a 5000 Ω resistor. The capacitor will discharge because the resistor provides a conducting pathway between the capacitor plates, but much more slowly than if the plates were connected by a wire. Let t=0 s be the instant the fully charged capacitor is first connected to the resistor. At what time has the capacitor voltage decreased by half, to 4.5 V?

(III) (a) Determine the currents I₁, I₂, and I₃ in Fig. 26–58. Assume the internal resistance of each battery is r = 1.0 Ω.

(b) What is the terminal voltage of the 6.0-V battery?

Three 45-Ω lightbulbs and three 65-Ω lightbulbs are connected in series. What is the total resistance if all six are wired in parallel?

A galvanometer has an internal resistance of 32 Ω and deflects full scale for a 48-μA current. Describe how to use this galvanometer to make a voltmeter to give a full scale deflection of 250 V.

You’ve made the finals of the Science Olympics! As one of your tasks, you’re given 1.0 g of aluminum and asked to make a wire, using all the aluminum, that will dissipate 7.5 W when connected to a 1.5 V battery. What length and diameter will you choose for your wire?

A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value?

A 15 μF capacitor charged to 12 V is discharged through a resistor. The energy stored in the capacitor decreases by 50% in 0.25 s. What is the value of the resistance?

Three 2.20-kΩ resistors can be connected together in four different ways, making combinations of series and/or parallel circuits. What are these four ways, and what is the net resistance in each case?

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]

(II) Determine the voltage across each resistor

A parallel-plate capacitor is filled with a dielectric of dielectric constant K and high resistivity ρ (it conducts very slightly). This capacitor can be modeled as a pure capacitance C in parallel with a resistance R. Assume a battery places a charge +Q and -Q on the capacitor’s opposing plates and is then disconnected. Show that the capacitor discharges with a time constant $\tau$ = K∊₀ρ (known as the dielectric relaxation time). Evaluate $\tau$ if the dielectric is glass with ρ = 1.0 x 10¹² Ωm and K = 5.0.