9.4 Ohm's law  (Page 2/7)

 Page 2 / 7

In this experiment, the voltage applied across the resistor varies from −10.00 to +10.00 V, by increments of 1.00 V. The current through the resistor and the voltage across the resistor are measured. A plot is made of the voltage versus the current, and the result is approximately linear. The slope of the line is the resistance, or the voltage divided by the current. This result is known as Ohm’s law    :

$V=IR,$

where V is the voltage measured in volts across the object in question, I is the current measured through the object in amps, and R is the resistance in units of ohms. As stated previously, any device that shows a linear relationship between the voltage and the current is known as an ohmic device. A resistor is therefore an ohmic device.

Measuring resistance

A carbon resistor at room temperature $\left(20\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\right)$ is attached to a 9.00-V battery and the current measured through the resistor is 3.00 mA. (a) What is the resistance of the resistor measured in ohms? (b) If the temperature of the resistor is increased to $60\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ by heating the resistor, what is the current through the resistor?

Strategy

(a) The resistance can be found using Ohm’s law. Ohm’s law states that $V=IR$ , so the resistance can be found using $R=V\text{/}I$ .

(b) First, the resistance is temperature dependent so the new resistance after the resistor has been heated can be found using $R={R}_{0}\left(1+\alpha \text{Δ}T\right)$ . The current can be found using Ohm’s law in the form $I=V\text{/}R$ .

Solution

1. Using Ohm’s law and solving for the resistance yields the resistance at room temperature:
$R=\frac{V}{I}=\frac{9.00\phantom{\rule{0.2em}{0ex}}\text{V}}{3.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\phantom{\rule{0.2em}{0ex}}\text{A}}=3.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}=3.00\phantom{\rule{0.2em}{0ex}}\text{k}\phantom{\rule{0.2em}{0ex}}\text{Ω}.$
2. The resistance at $60\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ can be found using $R={R}_{0}\left(1+\alpha \text{Δ}T\right)$ where the temperature coefficient for carbon is $\alpha =-0.0005$ . $R={R}_{0}\left(1+\alpha \text{Δ}T\right)=3.00\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\left(1-0.0005\left(60\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}-20\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}\right)\right)=2.94\phantom{\rule{0.2em}{0ex}}\text{k}\phantom{\rule{0.2em}{0ex}}\text{Ω}$ .
The current through the heated resistor is
$I=\frac{V}{R}=\frac{9.00\phantom{\rule{0.2em}{0ex}}\text{V}}{2.94\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{3}\phantom{\rule{0.2em}{0ex}}\text{Ω}\phantom{\rule{0.2em}{0ex}}}=3.06\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}\text{A}=3.06\phantom{\rule{0.2em}{0ex}}\text{mA}.$

Significance

A change in temperature of $40\phantom{\rule{0.2em}{0ex}}\text{°}\text{C}$ resulted in a 2.00% change in current. This may not seem like a very great change, but changing electrical characteristics can have a strong effect on the circuits. For this reason, many electronic appliances, such as computers, contain fans to remove the heat dissipated by components in the electric circuits.

Check Your Understanding The voltage supplied to your house varies as $V\left(t\right)={V}_{\text{max}}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\left(2\pi ft\right)$ . If a resistor is connected across this voltage, will Ohm’s law $V=IR$ still be valid?

Yes, Ohm’s law is still valid. At every point in time the current is equal to $I\left(t\right)=V\left(t\right)\text{/}R$ , so the current is also a function of time, $I\left(t\right)=\frac{{V}_{\text{max}}}{R}\phantom{\rule{0.2em}{0ex}}\text{sin}\phantom{\rule{0.2em}{0ex}}\left(2\pi ft\right)$ .

See how the equation form of Ohm’s law relates to a simple circuit. Adjust the voltage and resistance, and see the current change according to Ohm’s law. The sizes of the symbols in the equation change to match the circuit diagram.

Nonohmic devices do not exhibit a linear relationship between the voltage and the current. One such device is the semiconducting circuit element known as a diode. A diode    is a circuit device that allows current flow in only one direction. A diagram of a simple circuit consisting of a battery, a diode, and a resistor is shown in [link] . Although we do not cover the theory of the diode in this section, the diode can be tested to see if it is an ohmic or a nonohmic device.

does your app come with video lessons?
What is vector
Vector is a quantity having a direction as well as magnitude
Damilare
tell me about charging and discharging of capacitors
a big and a small metal spheres are connected by a wire, which of this has the maximum electric potential on the surface.
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
four effect of heat on substances
why we can find a electric mirror image only in a infinite conducting....why not in finite conducting plate..?
because you can't fit the boundary conditions.
Jorge
what is the dimensions for VISCOUNSITY (U)
Branda
what is thermodynamics
the study of heat an other form of energy.
John
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.
ing
It is abranch of physical chemistry which deals with the interconversion of all form of energy
Vishal
what is colamb,s law.?
it is a low studied the force between 2 charges F=q.q\r.r
Mostafa
what is the formula of del in cylindrical, polar media
prove that the formula for the unknown resistor is Rx=R2 x R3 divided by R3,when Ig=0.
what is flux
Total number of field lines crossing the surface area
Kamru
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
prince
what is temperature change
Celine
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
Celine
process whereby the degree of hotness of a body (or medium) changes
Salim
Q=mcΔT
Salim
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.
Salim
what was the temperature of the soft drink when it was removed ?
Salim
15 degree Celsius
Celine
15 degree
Celine
ok I think is just conversion
Salim
15 degree Celsius to Fahrenheit
Salim
0 degree Celsius = 32 Fahrenheit
Salim
15 degree Celsius = (15×1.8)+32 =59 Fahrenheit
Salim
I dont understand
Celine
the question said you should convert 15 degree Celsius to Fahrenheit
Salim
To convert temperatures in degrees Celsius to Fahrenheit, multiply by 1.8 (or 9/5) and add 32.
Salim
what is d final ans for Fahrenheit and Celsius
Celine
it said what is temperature change in Fahrenheit and Celsius
Celine
the 15 is already in Celsius
Salim
So the final answer for Fahrenheit is 59
Salim
what is d final ans for Fahrenheit and Celsius
Celine
what are the effects of placing a dielectric between the plates of a capacitor
increase the capacitance.
Jorge
besides increasing the capacitance, is there any?
Bundi
mechanical stiffness and small size
Jorge
so as to increase the capacitance of a capacitor
Rahma
also to avoid diffusion of charges between the two plate since they are positive and negative.
Prince
why for an ideal gas internal energy is directly proportional to thermodynamics temperature?
two charged particles are 8.45cm apart. They are moved and the force on each of them is found to have tripled. How far are they now?
what is flux
Bundi
Bundi, flux is the number of electric field crossing a surface area
Mubanga
you right
martin,F/F=(r×r)÷(r×r)
Mostafa