Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations.
Column I Column II A Drift Velocity P \(\frac{ m }{ ne ^{2} \rho}\) B Electrical Resistivity Q \(ne v_{ d }\) C Relaxation Period R \(\frac{ e E }{ m } \tau\) D Current Density S \(\frac{ E }{ J }\)
Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column - II gives some mathematical relations involving electrical quantities. Match Column - I and Column - II with appropriate relations.
| Column I | Column II | ||
|---|---|---|---|
| A | Drift Velocity | P | \(\frac{ m }{ ne ^{2} \rho}\) |
| B | Electrical Resistivity | Q | \(ne v_{ d }\) |
| C | Relaxation Period | R | \(\frac{ e E }{ m } \tau\) |
| D | Current Density | S | \(\frac{ E }{ J }\) |
- (A)-(R), (B)-(S), (C)-(P), (D)-(Q)
- (A)-(R), (B)-(S), (C)-(Q), (D)-(P)
- (A)-(R), (B)-(P), (C)-(S), (D)-(Q)
- (A)-(R), (B)-(Q), (C)-(S), (D)-(P)
The Correct Option is A
Solution and Explanation
To match the physical terms associated with the flow of current through a metallic conductor in Column I with the correct mathematical relations in Column II, let's analyze each term:
- Drift Velocity (A):
Drift velocity is the average velocity that a charged particle, such as an electron, attains due to an electric field. The formula for drift velocity (\(v_d\)) is given by: \(v_d = \frac{eE\tau}{m}\), where:
- \(e\) is the electron charge,
- \(E\) is the electric field,
- \(\tau\) is the relaxation time,
- \(m\) is the electron mass.
- Electrical Resistivity (B):
Electrical resistivity (\(\rho\)) is defined as a material's ability to resist the flow of electric current. The relation involving current density (\(J\)) is: \(\rho = \frac{E}{J}\), where \(E\) is the electric field. This matches option (S) in Column II. Thus, (B)-(S).
- Relaxation Period (C):
In the context of electrical conduction, the relaxation period or time (\(\tau\)) is the average time between subsequent collisions of electrons moving through a metal. It relates to the formula for resistivity: \(\rho = \frac{m}{ne^2\tau}\). Therefore, it matches with option (P) in Column II. Thus, (C)-(P).
- Current Density (D):
Current density (\(J\)) is the electric current per unit area of cross-section. The formula involving drift velocity is: \(J = nev_d\). This matches with option (Q) in Column II. Thus, (D)-(Q).
Therefore, the correct matching is (A)-(R), (B)-(S), (C)-(P), (D)-(Q), which is consistent with the given correct answer.
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Concepts Used:
Current Electricity
Current electricity is defined as the flow of electrons from one section of the circuit to another.
Types of Current Electricity
There are two types of current electricity as follows:
Direct Current
The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.
Alternating Current
The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.