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The graph shows voltage at several points in a circuit. The points are shown on the x-axis. The y-axis shows the voltage, which is 0 from origin to point a and rises linearly to E from a to b and then drops linearly to E minus I r from b to c. The voltage is constant from c to d and then drops linearly to 0 from d to e.
A graph of the voltage through the circuit of a battery and a load resistance. The electric potential increases the emf of the battery due to the chemical reactions doing work on the charges. There is a decrease in the electric potential in the battery due to the internal resistance. The potential decreases due to the internal resistance ( I r ) , making the terminal voltage of the battery equal to ( ε I r ) . The voltage then decreases by ( IR ). The current is equal to I = ε r + R .

The current through the load resistor is I = ε r + R . We see from this expression that the smaller the internal resistance r , the greater the current the voltage source supplies to its load R . As batteries are depleted, r increases. If r becomes a significant fraction of the load resistance, then the current is significantly reduced, as the following example illustrates.

Analyzing a circuit with a battery and a load

A given battery has a 12.00-V emf and an internal resistance of 0.100 Ω . (a) Calculate its terminal voltage when connected to a 10.00 - Ω load. (b) What is the terminal voltage when connected to a 0.500 - Ω load? (c) What power does the 0.500 - Ω load dissipate? (d) If the internal resistance grows to 0.500 Ω , find the current, terminal voltage, and power dissipated by a 0.500 - Ω load.


The analysis above gave an expression for current when internal resistance is taken into account. Once the current is found, the terminal voltage can be calculated by using the equation V terminal = ε I r . Once current is found, we can also find the power dissipated by the resistor.


  1. Entering the given values for the emf, load resistance, and internal resistance into the expression above yields
    I = ε R + r = 12.00 V 10.10 Ω = 1.188 A .

    Enter the known values into the equation V terminal = ε I r to get the terminal voltage:
    V terminal = ε I r = 12.00 V ( 1.188 A ) ( 0.100 Ω ) = 11.90 V .

    The terminal voltage here is only slightly lower than the emf, implying that the current drawn by this light load is not significant.
  2. Similarly, with R load = 0.500 Ω , the current is
    I = ε R + r = 12.00 V 0.600 Ω = 20.00 A .

    The terminal voltage is now
    V terminal = ε I r = 12.00 V ( 20.00 A ) ( 0.100 Ω ) = 10.00 V .

    The terminal voltage exhibits a more significant reduction compared with emf, implying 0.500 Ω is a heavy load for this battery. A “heavy load” signifies a larger draw of current from the source but not a larger resistance.
  3. The power dissipated by the 0.500 - Ω load can be found using the formula P = I 2 R . Entering the known values gives
    P = I 2 R = ( 20.0 A ) 2 ( 0.500 Ω ) = 2.00 × 10 2 W.

    Note that this power can also be obtained using the expression V 2 R or I V , where V is the terminal voltage (10.0 V in this case).
  4. Here, the internal resistance has increased, perhaps due to the depletion of the battery, to the point where it is as great as the load resistance. As before, we first find the current by entering the known values into the expression, yielding
    I = ε R + r = 12.00 V 1.00 Ω = 12.00 A .

    Now the terminal voltage is
    V terminal = ε I r = 12.00 V ( 12.00 A ) ( 0.500 Ω ) = 6.00 V ,

    and the power dissipated by the load is
    P = I 2 R = ( 12.00 A ) 2 ( 0.500 Ω ) = 72.00 W.

    We see that the increased internal resistance has significantly decreased the terminal voltage, current, and power delivered to a load.

Questions & Answers

define electric image.obtain expression for electric intensity at any point on earthed conducting infinite plane due to a point charge Q placed at a distance D from it.
Mateshwar Reply
explain the lack of symmetry in the field of the parallel capacitor
Phoebe Reply
pls. explain the lack of symmetry in the field of the parallel capacitor
does your app come with video lessons?
Ahmed Reply
What is vector
Ajibola Reply
Vector is a quantity having a direction as well as magnitude
tell me about charging and discharging of capacitors
Ahemen Reply
a big and a small metal spheres are connected by a wire, which of this has the maximum electric potential on the surface.
Bundi Reply
3 capacitors 2nf,3nf,4nf are connected in parallel... what is the equivalent capacitance...and what is the potential difference across each capacitor if the EMF is 500v
Prince Reply
equivalent capacitance is 9nf nd pd across each capacitor is 500v
four effect of heat on substances
Prince Reply
why we can find a electric mirror image only in a infinite conducting....why not in finite conducting plate..?
Rima Reply
because you can't fit the boundary conditions.
what is the dimensions for VISCOUNSITY (U)
what is thermodynamics
Aniket Reply
the study of heat an other form of energy.
heat is internal kinetic energy of a body but it doesnt mean heat is energy contained in a body because heat means transfer of energy due to difference in temperature...and in thermo-dynamics we study cause, effect, application, laws, hypothesis and so on about above mentioned phenomenon in detail.
It is abranch of physical chemistry which deals with the interconversion of all form of energy
what is colamb,s law.?
Muhammad Reply
it is a low studied the force between 2 charges F=q.q`\r.r
what is the formula of del in cylindrical, polar media
Birengeso Reply
prove that the formula for the unknown resistor is Rx=R2 x R3 divided by R3,when Ig=0.
what is flux
Bundi Reply
Total number of field lines crossing the surface area
Basically flux in general is amount of anything...In Electricity and Magnetism it is the total no..of electric field lines or Magnetic field lines passing normally through the suface
what is temperature change
a bottle of soft drink was removed from refrigerator and after some time, it was observed that its temperature has increased by 15 degree Celsius, what is the temperature change in degree Fahrenheit and degree Celsius
process whereby the degree of hotness of a body (or medium) changes
where The letter "Q" is the heat transferred in an exchange in calories, "m" is the mass of the substance being heated in grams, "c" is its specific heat capacity and the static value, and "ΔT" is its change in temperature in degrees Celsius to reflect the change in temperature.
what was the temperature of the soft drink when it was removed ?
15 degree Celsius
15 degree
ok I think is just conversion
15 degree Celsius to Fahrenheit
0 degree Celsius = 32 Fahrenheit
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
I dont understand
the question said you should convert 15 degree Celsius to Fahrenheit
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
what is d final ans for Fahrenheit and Celsius
it said what is temperature change in Fahrenheit and Celsius
the 15 is already in Celsius
So the final answer for Fahrenheit is 59
what is d final ans for Fahrenheit and Celsius
what are the effects of placing a dielectric between the plates of a capacitor
Bundi Reply
increase the capacitance.
besides increasing the capacitance, is there any?
mechanical stiffness and small size
so as to increase the capacitance of a capacitor
also to avoid diffusion of charges between the two plate since they are positive and negative.
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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