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Carbon-zinc dry cells (sometimes referred to as non-alkaline cells) have an emf of 1.54 V, and they are produced as single cells or in various combinations to form other voltages. (a) How many 1.54-V cells are needed to make the common 9-V battery used in many small electronic devices? (b) What is the actual emf of the approximately 9-V battery? (c) Discuss how internal resistance in the series connection of cells will affect the terminal voltage of this approximately 9-V battery.
What is the output voltage of a 3.0000-V lithium cell in a digital wristwatch that draws 0.300 mA, if the cell’s internal resistance is $2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\Omega $ ?
2.9994 V
(a) What is the terminal voltage of a large 1.54-V carbon-zinc dry cell used in a physics lab to supply 2.00 A to a circuit, if the cell’s internal resistance is $0\text{.}\text{100 \Omega}$ ? (b) How much electrical power does the cell produce? (c) What power goes to its load?
What is the internal resistance of an automobile battery that has an emf of 12.0 V and a terminal voltage of 15.0 V while a current of 8.00 A is charging it?
$0\text{.}\text{375}\phantom{\rule{0.25em}{0ex}}\Omega $
(a) Find the terminal voltage of a 12.0-V motorcycle battery having a $0\text{.}\text{600-\Omega}$ internal resistance, if it is being charged by a current of 10.0 A. (b) What is the output voltage of the battery charger?
A car battery with a 12-V emf and an internal resistance of $0\text{.}\text{050}\phantom{\rule{0.15em}{0ex}}\Omega $ is being charged with a current of 60 A. Note that in this process the battery is being charged. (a) What is the potential difference across its terminals? (b) At what rate is thermal energy being dissipated in the battery? (c) At what rate is electric energy being converted to chemical energy? (d) What are the answers to (a) and (b) when the battery is used to supply 60 A to the starter motor?
The hot resistance of a flashlight bulb is $2\text{.}\text{30}\phantom{\rule{0.15em}{0ex}}\Omega $ , and it is run by a 1.58-V alkaline cell having a $0\text{.}\text{100-\Omega}$ internal resistance. (a) What current flows? (b) Calculate the power supplied to the bulb using ${I}^{2}{R}_{\text{bulb}}$ . (c) Is this power the same as calculated using $\frac{{V}^{2}}{{R}_{\text{bulb}}}$ ?
(a) 0.658 A
(b) 0.997 W
(c) 0.997 W; yes
The label on a portable radio recommends the use of rechargeable nickel-cadmium cells (nicads), although they have a 1.25-V emf while alkaline cells have a 1.58-V emf. The radio has a $3\text{.}\text{20-\Omega}$ resistance. (a) Draw a circuit diagram of the radio and its batteries. Now, calculate the power delivered to the radio. (b) When using Nicad cells each having an internal resistance of $0\text{.}\text{0400 \Omega}$ . (c) When using alkaline cells each having an internal resistance of $0\text{.}\text{200 \Omega}$ . (d) Does this difference seem significant, considering that the radio’s effective resistance is lowered when its volume is turned up?
An automobile starter motor has an equivalent resistance of $0\text{.}\text{0500}\phantom{\rule{0.15em}{0ex}}\Omega $ and is supplied by a 12.0-V battery with a $0\text{.}\text{0100-\Omega}$ internal resistance. (a) What is the current to the motor? (b) What voltage is applied to it? (c) What power is supplied to the motor? (d) Repeat these calculations for when the battery connections are corroded and add $0\text{.}\text{0900}\phantom{\rule{0.15em}{0ex}}\Omega $ to the circuit. (Significant problems are caused by even small amounts of unwanted resistance in low-voltage, high-current applications.)
(a) 200 A
(b) 10.0 V
(c) 2.00 kW
(d) $0\text{.}\text{1000}\phantom{\rule{0.25em}{0ex}}\Omega ;\phantom{\rule{0.25em}{0ex}}\text{80}\text{.}\text{0 A, 4}\text{.}\text{0 V, 320 W}$
A child’s electronic toy is supplied by three 1.58-V alkaline cells having internal resistances of $0\text{.}\text{0200}\phantom{\rule{0.15em}{0ex}}\Omega $ in series with a 1.53-V carbon-zinc dry cell having a $0\text{.}\text{100-\Omega}$ internal resistance. The load resistance is $\text{10}\text{.}0\phantom{\rule{0.15em}{0ex}}\Omega $ . (a) Draw a circuit diagram of the toy and its batteries. (b) What current flows? (c) How much power is supplied to the load? (d) What is the internal resistance of the dry cell if it goes bad, resulting in only 0.500 W being supplied to the load?
(a) What is the internal resistance of a voltage source if its terminal voltage drops by 2.00 V when the current supplied increases by 5.00 A? (b) Can the emf of the voltage source be found with the information supplied?
(a) $0\text{.}\text{400 \Omega}$
(b) No, there is only one independent equation, so only $r$ can be found.
A person with body resistance between his hands of $\text{10}\text{.}0\phantom{\rule{0.25em}{0ex}}\text{k}\Omega $ accidentally grasps the terminals of a 20.0-kV power supply. (Do NOT do this!) (a) Draw a circuit diagram to represent the situation. (b) If the internal resistance of the power supply is $\text{2000}\phantom{\rule{0.15em}{0ex}}\Omega $ , what is the current through his body? (c) What is the power dissipated in his body? (d) If the power supply is to be made safe by increasing its internal resistance, what should the internal resistance be for the maximum current in this situation to be 1.00 mA or less? (e) Will this modification compromise the effectiveness of the power supply for driving low-resistance devices? Explain your reasoning.
Electric fish generate current with biological cells called electroplaques, which are physiological emf devices. The electroplaques in the South American eel are arranged in 140 rows, each row stretching horizontally along the body and each containing 5000 electroplaques. Each electroplaque has an emf of 0.15 V and internal resistance of $0\text{.}\text{25}\phantom{\rule{0.15em}{0ex}}\Omega $ . If the water surrounding the fish has resistance of $\text{800}\phantom{\rule{0.15em}{0ex}}\Omega $ , how much current can the eel produce in water from near its head to near its tail?
Integrated Concepts
A 12.0-V emf automobile battery has a terminal voltage of 16.0 V when being charged by a current of 10.0 A. (a) What is the battery’s internal resistance? (b) What power is dissipated inside the battery? (c) At what rate (in $\text{\xba}\text{C/min}$ ) will its temperature increase if its mass is 20.0 kg and it has a specific heat of $0\text{.}\text{300}\phantom{\rule{0.25em}{0ex}}\text{kcal/kg}\cdot \text{\xba}\text{C}$ , assuming no heat escapes?
Unreasonable Results
A 1.58-V alkaline cell with a $0\text{.}\text{200-\Omega}$ internal resistance is supplying 8.50 A to a load. (a) What is its terminal voltage? (b) What is the value of the load resistance? (c) What is unreasonable about these results? (d) Which assumptions are unreasonable or inconsistent?
(a) –0.120 V
(b) $-1\text{.}\text{41}\times {\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}\Omega $
(c) Negative terminal voltage; negative load resistance.
(d) The assumption that such a cell could provide 8.50 A is inconsistent with its internal resistance.
Unreasonable Results
(a) What is the internal resistance of a 1.54-V dry cell that supplies 1.00 W of power to a $\text{15}\text{.}\mathrm{0-\Omega}$ bulb? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
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