27. Resistors & DC Circuits

What is current and voltage across each resistor below?

What is the voltage of the battery below?

(II) A galvanometer has a sensitivity of 45kΩ/V and internal resistance 20.0 Ω. How could you make this into

(a) an ammeter that reads 1.0 A full scale, or

(II) 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

(b) a voltmeter to give a full scale deflection of 250 V.

(II) 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?

(II) 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 .

(II) 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 τ = K ∊₀ρ (known as the dielectric relaxation time). Evaluate τ if the dielectric is glass with ρ = 1.0 x 10¹² Ω•m and K = 5.0.

Cardiac defibrillators are discussed in Section 24–4. (a) 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?

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

(III) 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?

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

(II) 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.]

(III) 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?

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

(I) Three 45-Ω lightbulbs and three 65-Ω lightbulbs are connected in series.

(b) What is the total resistance if all six are wired in parallel?

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

(I) Three 45-Ω lightbulbs and three 65-Ω lightbulbs are connected in series.

(a) What is the total resistance of the circuit?

(III) If the 25-Ω resistor in Fig. 26–59 is shorted out (resistance = 0 ), what then would be the current through the 15-Ω resistor?

Cardiac defibrillators are discussed in Section 24–4. (b) The effective resistance of the human body is given in Section 26–6. If the defibrillator discharges with a time constant of 12 ms, what is the effective capacitance of the human body?

A typical voltmeter has an internal resistance of 10 MΩ and can only measure potential differences of up to several hundred volts. Figure 26–93 shows the design of a probe to measure a very high voltage V using a voltmeter. If you want the voltmeter to read 50 V when V = 50 kV , what value R should be used in this probe?

<IMAGE>

"The current through the 4.0 -kΩ resistor in Fig. 26–74 is 2.85 mA. What is the terminal voltage V_ba of the “unknown” battery? (There are two answers. Why?)

<IMAGE>"