27. Resistors & DC Circuits

A galvanometer has a sensitivity of 45kΩ/V and internal resistance 20.0 Ω. How could you make this into an ammeter that reads 1.0 A full scale?

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.

A milliammeter reads 25 mA full scale. It consists of a 0.20-Ω resistor in parallel with a 33-Ω galvanometer. How can you change this ammeter to a voltmeter giving a full scale reading of 25 V without taking the ammeter apart? What will be the sensitivity (Ω/V) of your voltmeter?

A 12.0-V battery (assume the internal resistance = 0) is connected to two resistors in series. A voltmeter whose internal resistance is 18.0 kΩ measures 5.5 V and 4.0 V, respectively, when connected across each of the resistors in turn. What is the resistance of each resistor?

Small changes in the length of an object can be measured using a strain gauge sensor, which is a wire that when undeformed has length ℓ₀, cross-sectional area A₀, and resistance R₀. This sensor is rigidly affixed to the object’s surface, aligning its length in the direction in which length changes are to be measured. As the object deforms, the length of the wire sensor changes by Δℓ, and the resulting change ΔR in the sensor’s resistance is measured. Assuming that as the solid wire is deformed to a length ℓ, its density and volume remain constant (only approximately valid), show that the strain ( = Δℓ / ℓ₀ ) of the wire sensor, and thus of the object to which it is attached, is approximately ΔR / 2R₀.

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.

Cardiac defibrillators are discussed in Section 24–4. Choose a value for the resistance so that the 1.4-μF capacitor can be charged to 3100 V in 2.0 seconds. Assume that this 3100 V is 95% of the full source voltage.

A 10.0-m length of wire consists of 5.0 m of copper followed by 5.0 m of aluminum, both of diameter 1.4 mm. A voltage difference of 75 mV is placed across the composite wire. (a) What is the total resistance (sum) of the two wires? (b) What is the current through the wire? (c) What are the voltages across the aluminum part and across the copper part?

A 2.5-kΩ and a 3.7-kΩ resistor are connected in parallel; this combination is connected in series with a 1.4-kΩ resistor. If each resistor is rated at 1.0 W (maximum without overheating), what is the maximum voltage that can be applied across the whole network?

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?

Neglect the internal resistance of a battery unless the Problem refers to it. Two resistors when connected in series to a 120-V line use one-fourth the power that is used when they are connected in parallel. If one resistor is 4.3 kΩ, what is the resistance of the other?

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?

Three 45-Ω lightbulbs and three 65-Ω lightbulbs are connected in series. What is the total resistance of the circuit?

To which two points in the circuit of FIGURE P28.45 should a 12 V battery be connected to dissipate the most power?

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?