Examples of Calculating Power in DC Circuits

📚 Quick Study Guide: Calculating Power in DC Circuits

• 💡 What is Power? In a DC circuit, electrical power ($P$) is the rate at which electrical energy is converted into another form of energy (like heat, light, or mechanical motion). Its standard unit is the Watt (W).
• 🔢 The Fundamental Power Formula: The most basic way to calculate power is using the current ($I$) and voltage ($V$).
  • $P = IV$
  • Where:
    • $P$ is Power in Watts (W)
    • $I$ is Current in Amperes (A)
    • $V$ is Voltage in Volts (V)
• ⚡ Power using Current and Resistance: If you know the current ($I$) and the resistance ($R$), you can calculate power directly.
  • $P = I^2R$
  • Where:
    • $P$ is Power in Watts (W)
    • $I$ is Current in Amperes (A)
    • $R$ is Resistance in Ohms ($\Omega$)
• 🔌 Power using Voltage and Resistance: When you have the voltage ($V$) across a component and its resistance ($R$), this formula is very useful.
  • $P = \frac{V^2}{R}$
  • Where:
    • $P$ is Power in Watts (W)
    • $V$ is Voltage in Volts (V)
    • $R$ is Resistance in Ohms ($\Omega$)
• ⚖️ Relationship with Ohm's Law: All three power formulas are derived from Ohm's Law ($V = IR$). You can use Ohm's Law to find a missing variable before applying a power formula, or substitute it directly into $P=IV$ to get the other two forms.
• 📏 Units are Key! Always ensure your units are consistent (Volts, Amperes, Ohms, Watts) before calculating. If you have milliamps or kilovolts, convert them first!
• ✅ Summary of Formulas:
  • $P = IV$
  • $P = I^2R$
  • $P = \frac{V^2}{R}$

🧠 Practice Quiz

Test your understanding of power calculations in DC circuits!

1. A simple DC circuit has a voltage source of $12 \text{ V}$ and a current of $2 \text{ A}$ flowing through it. What is the total power dissipated by the circuit?

   1. $6 \text{ W}$
   2. $10 \text{ W}$
   3. $24 \text{ W}$
   4. $144 \text{ W}$

2. A resistor with a resistance of $10 \, \Omega$ has $3 \text{ A}$ of current passing through it. What is the power dissipated by the resistor?

   1. $30 \text{ W}$
   2. $90 \text{ W}$
   3. $100 \text{ W}$
   4. $120 \text{ W}$

3. An incandescent light bulb connected to a $24 \text{ V}$ DC source has a resistance of $48 \, \Omega$. What is the power rating of the bulb?

   1. $0.5 \text{ W}$
   2. $12 \text{ W}$
   3. $24 \text{ W}$
   4. $1152 \text{ W}$

4. If a DC motor consumes $60 \text{ W}$ of power when operating with a $5 \text{ A}$ current, what is the voltage across the motor?

   1. $12 \text{ V}$
   2. $300 \text{ V}$
   3. $0.083 \text{ V}$
   4. $65 \text{ V}$

5. A $100 \text{ W}$ heating element is designed to operate from a $10 \text{ V}$ DC supply. What is its resistance?

   1. $1 \, \Omega$
   2. $10 \, \Omega$
   3. $0.1 \, \Omega$
   4. $100 \, \Omega$

6. Which of the following units is NOT a standard unit for power?

   1. Watt (W)
   2. Joule per second (J/s)
   3. Volt-Ampere (VA)
   4. Ampere-Ohm (A$\Omega$)

7. A circuit has a $10 \text{ V}$ source and a total resistance of $5 \, \Omega$. What is the total power dissipated in the circuit?

   1. $0.5 \text{ W}$
   2. $2 \text{ W}$
   3. $20 \text{ W}$
   4. $50 \text{ W}$