Electric current is a fundamental concept in the field of electrical engineering and physics. It refers to the flow of electric charge through a conductor or a circuit. Below are some essential aspects of electric current.

Definition

Electric current can be defined as the rate of flow of electric charge past a point or a region. Mathematically, it is given by:

\[ I = \frac{{dq}}{{dt}} \]

where \( I \) is the current, \( dq \) is the change in charge, and \( dt \) is the change in time.

Direction

The direction of electric current is conventionally taken as the direction in which positive charges flow. In metals, the charge carriers are actually electrons, which are negatively charged, so they flow in the opposite direction to conventional current.

Units

The SI unit of electric current is the Ampere (A). One Ampere is equivalent to one Coulomb of charge passing through a point in one second.

Types of Current

1. Direct Current (DC): This is a unidirectional flow of electric charge. DC current is constant and flows in one direction.

2. Alternating Current (AC): AC current changes direction periodically. The voltage alternates in a sinusoidal or other periodic forms.

Ohm’s Law

Ohm’s law is a fundamental relationship that connects current, voltage, and resistance. It’s given by:

\[ V = I \cdot R \]

where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance.

Applications

Electric current is an essential part of modern life, powering everything from household appliances to industrial machinery. It’s used in various applications like lighting, heating, transportation, and much more.

Conclusion

Understanding electric current is vital for those studying or working in the fields of physics and engineering. Its properties and behavior in various materials lead to the extensive applications of electricity in our daily lives. Continuous research and innovation are expanding the capabilities and efficiencies of electric current in various technological areas, contributing to the advancement of society.

**PROBLEMS AND SOLUTIONS**

1. Problem: Calculate the current if 10 Coulombs of charge pass through a point in 2 seconds.

Solution: \( I = \frac{{10}}{{2}} = 5 \, \text{A} \)

2. Problem: Find the voltage across a 5-ohm resistor carrying a current of 2 Amperes.

Solution: \( V = 2 \times 5 = 10 \, \text{V} \)

3. Problem: Determine the current when 20 Coulombs flow through a wire in 4 seconds.

Solution: \( I = \frac{{20}}{{4}} = 5 \, \text{A} \)

4. Problem: If a 15-ohm resistor has a voltage of 30 volts across it, what is the current?

Solution: \( I = \frac{{30}}{{15}} = 2 \, \text{A} \)

5. Problem: Calculate the current flowing through a wire if 25 Coulombs of charge pass through it in 5 seconds.

Solution: \( I = \frac{{25}}{{5}} = 5 \, \text{A} \)

6. Problem: Find the resistance of a circuit element if a current of 3 Amperes flows with a voltage of 15 volts.

Solution: \( R = \frac{{15}}{{3}} = 5 \, \Omega \)

7. Problem: Determine the time taken for 50 Coulombs of charge to pass a point at a current of 10 Amperes.

Solution: \( t = \frac{{50}}{{10}} = 5 \, \text{s} \)

8. Problem: Calculate the charge passed through a point in a circuit if a current of 4 Amperes flows for 3 seconds.

Solution: \( q = 4 \times 3 = 12 \, \text{C} \)

9. Problem: If the voltage across a 10-ohm resistor is 40 volts, what is the current?

Solution: \( I = \frac{{40}}{{10}} = 4 \, \text{A} \)

10. Problem: Determine the voltage across a 6-ohm resistor carrying a current of 5 Amperes.

Solution: \( V = 5 \times 6 = 30 \, \text{V} \)

11. Problem: Calculate the current flowing through a 12-ohm resistor if the voltage across it is 24 volts.

Solution: \( I = \frac{{24}}{{12}} = 2 \, \text{A} \)

12. Problem: Find the resistance of a circuit if a current of 6 Amperes flows with a voltage of 18 volts.

Solution: \( R = \frac{{18}}{{6}} = 3 \, \Omega \)

13. Problem: Determine the voltage across an 8-ohm resistor carrying a current of 3 Amperes.

Solution: \( V = 3 \times 8 = 24 \, \text{V} \)

14. Problem: Calculate the current if 30 Coulombs of charge pass through a point in 6 seconds.

Solution: \( I = \frac{{30}}{{6}} = 5 \, \text{A} \)

15. Problem: If a 20-ohm resistor has a voltage of 60 volts across it, what is the current?

Solution: \( I = \frac{{60}}{{20}} = 3 \, \text{A} \)

16. Problem: Calculate the time taken for 80 Coulombs of charge to pass a point at a current of 8 Amperes.

Solution: \( t = \frac{{80}}{{8}} = 10 \, \text{s} \)

17. Problem: Determine the resistance of a circuit if a current of 4 Amperes flows with a voltage of 20 volts.

Solution: \( R = \frac{{20}}{{4}} = 5 \, \Omega \)

18. Problem: Find the current flowing through a wire if 15 Coulombs of charge pass through it in 3 seconds.

Solution: \( I = \frac{{15}}{{3}} = 5 \, \text{A} \)

19. Problem: If the voltage across a 5-ohm resistor is 25 volts, what is the current?

Solution: \( I = \frac{{25}}{{5}} = 5 \, \text{A} \)

20. Problem: Calculate the charge passed through a point in a circuit if a current of 6 Amperes flows for 2 seconds.

Solution: \( q = 6 \times 2 = 12 \, \text{C} \)

These problems and solutions cover the fundamental aspects of electric current, such as calculations involving Ohm’s law and the relation between charge, current, and time.