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Summary

  • All voltage sources have two fundamental parts: a source of electrical energy that has a characteristic electromotive force (emf), and an internal resistance r . The emf is the work done per charge to keep the potential difference of a source constant. The emf is equal to the potential difference across the terminals when no current is flowing. The internal resistance r of a voltage source affects the output voltage when a current flows.
  • The voltage output of a device is called its terminal voltage V terminal and is given by V terminal = ε I r , where I is the electric current and is positive when flowing away from the positive terminal of the voltage source and r is the internal resistance.

Conceptual questions

What effect will the internal resistance of a rechargeable battery have on the energy being used to recharge the battery?

Some of the energy being used to recharge the battery will be dissipated as heat by the internal resistance.

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A battery with an internal resistance of r and an emf of 10.00 V is connected to a load resistor R = r . As the battery ages, the internal resistance triples. How much is the current through the load resistor reduced?

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Show that the power dissipated by the load resistor is maximum when the resistance of the load resistor is equal to the internal resistance of the battery.

P = I 2 R = ( ε r + R ) 2 R = ε 2 R ( r + R ) −2 , d P d R = ε 2 [ ( r + R ) −2 2 R ( r + R ) −3 ] = 0 , [ ( r + R ) 2 R ( r + R ) 3 ] = 0 , r = R

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Problems

A car battery with a 12-V emf and an internal resistance of 0.050 Ω 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 into chemical energy?

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The label on a battery-powered radio recommends the use of rechargeable nickel-cadmium cells (nicads), although they have a 1.25-V emf, whereas alkaline cells have a 1.58-V emf. The radio has a 3.20 Ω 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 0.0400 Ω , and (c) when using alkaline cells, each having an internal resistance of 0.200 Ω . (d) Does this difference seem significant, considering that the radio’s effective resistance is lowered when its volume is turned up?

a.
The figure shows a circuit with an emf source ε, resistor r and voltmeter V
b. 0.476W; c. 0.691 W; d. As R L is lowered, the power difference decreases; therefore, at higher volumes, there is no significant difference.

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An automobile starter motor has an equivalent resistance of 0.0500 Ω and is supplied by a 12.0-V battery with a 0.0100 - Ω 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 0.0900 Ω to the circuit. (Significant problems are caused by even small amounts of unwanted resistance in low-voltage, high-current applications.)

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(a) What is the internal resistance of a voltage source if its terminal potential 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. 0.400 Ω ; b. No, there is only one independent equation, so only r can be found.

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A person with body resistance between his hands of 10.0 k Ω 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 2000 Ω , 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.

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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 ° C / min ) will its temperature increase if its mass is 20.0 kg and it has a specific heat of 0.300 kcal/kg · ° C , assuming no heat escapes?

a. 0.400 Ω ; b. 40.0 W; c. 0.0956 °C/min

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Questions & Answers

two point charges +30c and +10c are separated by a distance of 80cm,compute the electric intensity and force on a +5×10^-6c charge place midway between the charges
Tijani Reply
what is the difference between temperature and heat
Ishom Reply
Heat is the condition or quality of being hot While Temperature is ameasure of cold or heat, often measurable with a thermometer
Abdul
Temperature is the one of heat indicators of materials that can be measured with thermometers, and Heat is the quantity of calor content in material that can be measured with calorimetry.
Gamma
2. A brass rod of length 50cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°c( degree Celsius) if the original length are 40°c(degree Celsius) is there at thermal stress developed at the junction? The end of the rod are free to expand (coefficient of linear expansion of brass = 2.0×10^-5, steel=1.2×10^-5k^1)
TONEJIT Reply
A charge insulator can be discharged by passing it just above a flame. Explain.
Mudassar Reply
of the three vectors in the equation F=qv×b which pairs are always at right angles?
DRASHTI Reply
what is an ideal gas?
Justine Reply
What is meant by zero Kelvin ?
Justine
Why does water cool when put in the pot ?
Justine
when we pour the water in a vessel(pot) the hot body(water) loses its heat to the surrounding in order to maintain thermal equilibrium.Thus,water cools.
rupendra
when we drop water in the pot, the pot body loses heat to surrounded in order to maintain thermal equilibrium thus,water cool.
Srabon
types of thermometer?
yemisi Reply
thermometer, Radiation thermometer and vapour pressure thermometer.liquid thermometer use thermometric liquid like mercury ,alcohol etc.
rupendra
liqid thermometer ,gas thermometer, resitance thermometer,thermo electric thermometer , radiation thermometer andvapour pressure thermometer
rupendra
calculate the quantity of heat required to rise the temperature of 1gmail of ice _10 to 110
Dargu Reply
A 40cm tall glass is filled with water to a depth of 30cm. A.what is the gauge pressure at the bottom of the glass? B.what is the absolute pressure at the bottom of the glass?
Abdulaziz Reply
A glass bottle full of mercury has mass 50g when heated through 35degree, 2.43g of mercury was expelled. Calculate the mass of the mercury remaining in the bottle
Anjorin Reply
Two electric point charges Q=2micro coulomb are fixed in space a distance 2.0cm apart. calculate the electric potential at the point p located a distance d/2 above the central point between two charges
Abdul Reply
what is wave
Ahmed Reply
A wave is a periodic disturbance which travel with a finite velocity and remains unchanged in type as it travels.
Justine
What's a wave motion?
Justine
What is charge bodies
Oje Reply
which have free elections
Usman
Show that if a vector is gradient of a scaler function then its line around a closed path is zero
Pak
Charge bodies are those which have free electons
Pak
the melting point of gold is 1064degree cencius and is boiling point is 2660 degree cenciu
Ilyas Reply
is Thomas's young experiment interference experiment or diffraction experiment or both
Ilyas Reply
An aqueous solution is prepared by diluting 3.30 mL acetone (d = 0.789 g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?
eugene
A 4.0kg mess kit sliding on a fractionless surface explodes into two 2.0 kg parts.3.0 m/s due to north and 0.5 m/s 30 degree north of east. what is the speed of the mess kit
Shahid
Practice Key Terms 5

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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