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Chapter 18: Problem 103

In a pacemaker used by a heart patient, a capacitor with a capacitance of $25 \mu \mathrm{F}\( is charged to \)1.0 \mathrm{V}$ and then discharged through the heart every 0.80 s. What is the average discharge current?

Short Answer

Expert verified
Answer: The average discharge current is \(31.25\mu \mathrm{A}\).

Step by step solution

01

Calculate the charge stored in the capacitor

Using the formula for the charge stored in a capacitor, Q = CV, we can find the charge Q stored in the capacitor. In this case, the capacitance C is given as \(25\mu \mathrm{F}\) and the voltage V is given as \(1.0\mathrm{V}\). $$ Q = CV = (25\mu \mathrm{F})(1.0 \mathrm{V}) = 25\mu \mathrm{C} $$
02

Calculate the average discharge current

To calculate the average discharge current, we can divide the charge Q by the discharge time interval t, which is given as \(0.80\mathrm{s}\). $$ I_\text{avg} = \frac{Q}{t} = \frac{25\mu \mathrm{C}}{0.80\mathrm{s}} = 31.25\mu \mathrm{A} $$ The average discharge current is \(31.25\mu \mathrm{A}\).

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Most popular questions from this chapter

A 20 - \(\mu\) F capacitor is discharged through a 5 -k\Omega resistor. The initial charge on the capacitor is \(200 \mu \mathrm{C}\) (a) Sketch a graph of the current through the resistor as a function of time. Label both axes with numbers and units. (b) What is the initial power dissipated in the resistor? (c) What is the total energy dissipated?
(a) In a charging \(R C\) circuit, how many time constants have elapsed when the capacitor has \(99.0 \%\) of its final charge? (b) How many time constants have elapsed when the capacitor has \(99.90 \%\) of its final charge? (c) How many time constants have elapsed when the current has \(1.0 \%\) of its initial value?
A galvanometer has a coil resistance of \(50.0 \Omega\). It is to be made into an ammeter with a full-scale deflection equal to \(10.0 \mathrm{A} .\) If the galvanometer deflects full scale for a current of \(0.250 \mathrm{mA},\) what size shunt resistor should be used?
Near Earth's surface the air contains both negative and positive ions, due to radioactivity in the soil and cosmic rays from space. As a simplified model, assume there are 600.0 singly charged positive ions per \(\mathrm{cm}^{3}\) and 500.0 singly charged negative ions per \(\mathrm{cm}^{3} ;\) ignore the presence of multiply charged ions. The electric field is $100.0 \mathrm{V} / \mathrm{m},$ directed downward. (a) In which direction do the positive ions move? The negative ions? (b) What is the direction of the current due to these ions? (c) The measured resistivity of the air in the region is $4.0 \times 10^{13} \Omega \cdot \mathrm{m} .$ Calculate the drift speed of the ions, assuming it to be the same for positive and negative ions. [Hint: Consider a vertical tube of air of length \(L\) and cross-sectional area \(A\) How is the potential difference across the tube related to the electric field strength?] (d) If these conditions existed over the entire surface of the Earth, what is the total current due to the movement of ions in the air?
The label on a \(12.0-\mathrm{V}\) truck battery states that it is rated at 180.0 A-h (ampere-hours). Treat the battery as ideal. (a) How much charge in coulombs can be pumped by the battery? [Hint: Convert A to A-s.] (b) How much electric energy can the battery supply? (c) Suppose the radio in the truck is left on when the engine is not running. The radio draws a current of 3.30 A. How long does it take to drain the battery if it starts out fully charged?
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