27. Resistors & DC Circuits

Electricity can be a hazard in hospitals, particularly to patients who are connected to electrodes, such as an ECG. Suppose that the motor of a motorized bed shorts out to the bed frame, and the bed frame’s connection to a ground has broken (or was not there in the first place). If a nurse touches the bed and the patient at the same time, the nurse becomes a conductor and a complete circuit can be made through the patient to ground through the ECG apparatus. This is shown schematically in Fig. 26–79. Calculate the current through the patient.

A sequence of potential differences V is applied across a wire ( diameter = 0.32 mm, length = 11cm) and the resulting currents I are measured as follows: Plot I vs. V. Based on this plot, can you conclude that the wire obeys Ohm’s law (i.e., did you obtain a straight line with the expected y-intercept, within the values of the significant figures)? If so, determine the wire’s resistance R.

A zener diode voltage regulator is shown in Fig. 40–55. Suppose that R = 2.80 kΩ and that the diode breaks down at a reverse voltage of 130 V. (The current increases rapidly at this point, as shown on the far left of Fig. 40–38 at a voltage of -12V on that diagram.) The diode is rated at a maximum current of 120 mA. (a) If R_load = 21.0 kΩ, over what range of supply voltages will the circuit maintain the output voltage at 130 V? (b) If the supply voltage is 275 V, over what range of load resistance will the voltage be regulated?

(a) What is the equivalent resistance of the circuit shown in Fig. 26–80? (b) What is the current in the 18-Ω resistor? (c) What is the current in the 12-Ω resistor? (d) What is the power dissipation in the 4.5-Ω resistor?

(II) An ammeter whose internal resistance is 53 Ω reads 5.25 mA when connected in a circuit containing a battery and two resistors in series whose values are 760 Ω and 480 Ω. What is the actual current when the ammeter is absent?

(II) What is the internal resistance of a 12.0-V car battery whose terminal voltage drops to 8.2 V when the starter motor draws 95 A? What is the resistance of the starter?

A battery produces 40.8 V when 7.10 A is drawn from it, and 47.3 V when 2.80 A is drawn. What are the emf and internal resistance of the battery?

Electrocardiographs are often connected as shown in Fig. 26–78. The lead wires to the legs are said to be capacitively coupled. A time constant of 3.0 s is typical and allows rapid changes in potential to be recorded accurately. If C = 3.0μF, what value must R have? [Hint: Consider each leg as a separate circuit.]

Electronic devices often use an RC circuit to protect against power outages as shown in Fig. 26–84. (a) If the protector circuit is supposed to keep the supply voltage at least 75% of full voltage for as long as 0.20 s, how big a resistance R is needed? The capacitor is 7.6 μF. Assume the attached “electronics” draws negligible current. (b) Between which two terminals should the device be connected, a and b, b and c, or a and c?

Imagine that a steady current I flows in a straight cylindrical wire of radius R₀ and resistivity ρ.

(a) If the current is then changed at a rate dI/dt, show that a displacement current ID exists in the wire of magnitude ε₀ρ(dI/dt).

(b) If the current in a copper wire is changed at the rate of 1.0 A/ms, determine the magnitude of ID.

(c) Determine the magnitude of the magnetic field BD created by ID at the surface of a copper wire with R₀ = 1.00 mm. Compare (as a ratio) BD with the field created at the surface of the wire by a steady current of 1.0 A.

Draw a circuit diagram for the circuit of FIGURE EX28.1.

A capacitor is discharged through a 100 Ω resistor. The discharge current decreases to 25% of its initial value in 2.5 ms. What is the value of the capacitor?