Electric Current and Ohm's law Test - 1

• Electric current: The rate of flow of electric charge is called electric current.
  • The SI unit of electric current is Ampere (A)

Hence, Electric current (I) = Q/t = Charge/time

EXPLANATION:

• The passage of current is due to the flow of positive charges. This is what we call the conventional flow of current, i.e. in the direction of flow of positive charges.
• The direction of the conventional current corresponds to the direction of positive charge which is from higher potential(positive) to lower potential(negative).
• After the discovery of electrons, it was observed that electrons are the particles that flow in a conductor.
• Electrons being negatively charged flow from the negative terminal to the positive terminal of the voltage source. So, the actual direction of the current should be from the negative to the positive terminal.
• Electric current is associated with the movement of electrons which is from lower potential(negative) to higher potential(positive), therefore, the direction of electric current is opposite to that of conventional current.
• Thus the direction of electric current is always opposite to the direction of conventional current in metallic conductors. So option 1 is correct.

Resistance is given by

\(R = \frac{V}{I}\)

From the graph of the I-V

\(Slope = \frac{I}{V} = \frac{1}{R}\)

Thus larger the slope smaller is the resistance

Order of increasing slope is

R₃ < R₂ < R₁

Order of increasing resistance is

CONCEPT:

Electric Current: It is defined as the net amount of electric charge(q) that flows through a cross-section of a conductor in an electric circuit in a per unit time(t).

The SI unit of electric current is Ampere(A).

Electric current (I) = Electric charge (q)/Time (t)

CALCULATION:

Given that:

⇒ Charge(q) = 20 Coulomb.

⇒ Time(t) = 1 seconds.

⇒ Electric Current(I) = ?

⇒ By using the formula:

Current (I) = q/I = 20/1

⇒ I = 20 Ampere.

So option 1 is correct.

CONCEPT:

• Ohm’s law: At constant temperature, the current flowing through a resistance is directly proportional to the potential difference across its end.

V = R I

Where V is potential difference, R is resistance and I is current flowing.

• Ohmic resistance: The resistance that follows ohm’s law is called ohmic resistance.
• All resistance don’t follow ohm’s law.

EXPLANATION:

• Since ohm’s law is valid for constant resistance. If we change the temperature then the resistance of the conductor will change and that will change the relation between current and potential difference. So statement 2 is true and statement 3 is wrong. So option 3 is correct.
• It is valid for ohmic resistance. So statement 1 is true

CONCEPT:

Electric current:

• The flow of electric charges through a conductor constitutes an electric current.
• Quantitatively, electric current in a conductor across an area held perpendicular to the direction of flow of charge is defined as the amount of charge flowing across that area per unit time i.e.,

\({\rm{Electric\;curernt\;}}\left( {\rm{I}} \right) = \frac{{{\rm{Electric\;charge}}\;\left( {\rm{Q}} \right)}}{{{\rm{Time\;}}\left( {\rm{t}} \right)}}\)

• SI unit of current is ampere and it is denoted by the letter A.

EXPLAINATION:

• In solids valence electrons freely move throughout the conductor, i.e., valence electrons are not attached to the atoms.
• When an electric field is applied, these valence electrons start flowing in a particular direction constituting the electric current. Therefore option 3 is correct. 

Important Points

• As the charge may be flowing in different directions at a particular time and space, so we consider the net flow of charge, i.e,         

\({\rm{Electric\;curernt\;}}\left( {\rm{I}} \right) = \frac{{{\rm{Total \, Electric\;charge}}\;\left( {\rm{Q}} \right)}}{{{\rm{Time\;}}\left( {\rm{t}} \right)}}\)                       

•  q+ is the positive charge flowing and if q- is the negative charge flowing, the net charge q = q+ - q-
•  In case charge flowing through an area varies with time, i.e., for non-steady current, we have

\(Electric \,\,current (I)=\frac{dq}{dt}\)

Additional Information

• Valence electrons move opposite to the direction of current flow. 
• The direction of current flow is in the direction of the electric field.
• Current carriers in liquids- positively and negatively charged ion.
• Current carriers in gasses- positive ions and electrons.

Concept:

• Drift Velocity: The average speed of electrons by which they slowly move inside a conductor under influence of an applied electric field is called drift velocity.
  • Drift velocity of the electrons is calculated by:

\(v_d=\frac{I}{neA}\)

I is current in the conductor, e is the electronic charge, n is the number of free electrons per unit volume A is cross-sectional Area.

Calculation:

Given,

The number of free electrons per unit volume n = 8.4 × 10 ²² / cm ³ 

Current I = 1.344 A

Cross-sectional Area A = 1 mm² = 10 ^-2 cm ²

Electronic charge e = 1.602 × 10 ^-19 C

Drift velocity from the above expression will be

\(v_d = \frac{1.344}{(8.4 \times 10^{22})(1.6 \times 10^{-19})(10^{-2})}\)

⇒ v_d = 10 ^-2 cm / sec

1 cm = 10 mm

So drift velocity (mm /sec) is

v_d = 10 -1 mm / sec

So, correct option is 0.1 mm per sec

• Electric current: The rate of flow of electric charge is called electric current.
  • The SI unit of electric current is Ampere (A)

Hence, Electric current (I) = Q/t = Charge/time

Electric charge (Q) = Electric current (I) × Time (t)

CALCULATION:​

Given that:

Current (I) = 4 A

Time (t) = 3 sec

The formula for calculating charge is Q = I × t

Q = 4 x 3 = 12 C

So electric charge flew (Q) = 12 C. Hence option 4 is correct.

CONCEPT:

• Drift velocity: The average velocity attained by charged particles, (eg. electrons) in a material due to an electric field.
  • Subatomic particles like electrons move in random directions all the time.
  • When electrons are subjected to an electric field they do move randomly, but they slowly drift in one direction, in the direction of the electric field applied.
•  The mathematical expression of drift velocity is 

\(v_d=\frac{-eEτ}{m}\)

Here negative sign shows that drift velocity is opposite to the direction of the electric field.

Where e = charge on electron, m = mass of electron, E = Electric field and τ = avegrage relaxtion time 

• The current in a metallic conductor is given by

⇒ I = neAV_d

Where n  = number of charge carriers, e =  Charge, A = Area, V_d = Drift velocity

EXPLANATION:

• The current in a metallic conductor is given by

⇒ I = neAV_d

Where n  = number of charge carriers, e =  Charge, A = Area, V_d = Drift velocity

• The conductors are abundant in the concentration of charge (electron) carriers, a conductor has a charge carrier density ≈ 10²⁸ Cm^-3. This much abundant density of charge carriers   makes the electric current higher in magnitude even the drift velocity is small.
• Hence, option 4 is the answer.

CONCEPT:

• Ohm’s law: At constant temperature, the potential difference across a current-carrying wire is directly proportional to the current flowing through it.

          i.e. V = IR

Where V = potential difference, R = resistance and I = current.

EXPLANATION:

Given - V = 6 V and I = 0.4 A

• According to ohm's law, V = IR
• The above equation can be written for resistance as

\(\Rightarrow R = \frac{V}{I}=\frac{6}{0.4\times 10^{-3}}=15\times 10^{3}\, \Omega=15\, k\Omega\)

Explanation:

Electric Current: The flow of electric charge per unit time is known as electric current

• If one coulomb of charge crosses an area in one second, then the current thought that area is one Ampere(A) 
• SI unit of current is Ampere (A) or coulomb per second 

\(⇒ I = \frac{Q}{T} \)

Where I = Electric current, Q = Electric charge, T = Time

• 1 μA = 10-6 A
• Electric current is a scalar quantity
• Although, Electric current has both magnitude and direction yet it is a scalar quantity. This is because the law of ordinary Algebra is used to add electric current and the law of vector addition is not applicable to the addition of electric.
• An ammeter needs to be connected in series in an electrical circuit to determine how many amperes of current is flowing in the electric circuit.

​Quantisation of charge: Experimentally it is established that all free charges are integral multiples of a basic unit of charge denoted by e. This basic unit of charge is the charge that an electron or proton carries. Thus charge q on a body is always given by

q = ne

Where n = integer, e = 1.6 × 10^-19 C

For 1 C

1 = n × 1.6 × 10-19 

n = 625 × 1016 

n = 6.25 × 1018