ch 22 sec 1_Current_and_Circuits w 8 tr 2

Formulas and Example Problems for Electric Current and Circuits

1. Circuit Not Working

• Formula: Ohm's Law: V = I * R

• Example Problem: A circuit has a resistance of 10 ohms and the voltage supply is 20 volts. What is the current flowing through the circuit?

  • Solution:

    • Using Ohm's Law: V = I * R

    • Rearranging gives us: I = V / R

    • Current, I = 20V / 10Ω = 2A

2. Overheating Resistors

• Formula: Power Dissipation: P = I² * R

• Example Problem: If the current through a resistor is 3A and the resistance is 5 ohms, what is the power dissipated by the resistor?

  • Solution:

    • P = I² * R

    • P = (3A)² * 5Ω = 9 * 5 = 45 Watts

3. Inconsistent Current Flow

• Formula: Ohm's Law: I = V / R

• Example Problem: A circuit section has a voltage of 15 volts and a resistance of 3 ohms. What is the current?

  • Solution:

    • I = V / R

    • I = 15V / 3Ω = 5A

4. Voltage Drops

• Formula: Kirchhoff's Voltage Law: ΣV = 0

• Example Problem: In a loop, you measure voltage sources of 10V and 5V, and drop across resistors of 4V and 6V. Verify if the circuit obeys Kirchhoff's Law.

  • Solution:

    • ΣV = 10V - 4V - 5V - 6V = -5V

    • The sum should equal zero; thus, the measured values indicate an error in circuit design.

5. Short Circuits

• Formula: Current: I = V / R

• Example Problem: A circuit with a supply voltage of 12V causes a short with negligible resistance. What would be the current?

  • Solution:

    • I = V / R

    • If we assume R approaches 0 (hypothetical), I would approach infinity, indicating a fault in the circuit that needs to be addressed.