Electric Power - AP Physics 2

1. How is power related to current and voltage in an AC circuit?

   $P = VI \cos \phi$. AC power includes the phase angle factor.

2. Calculate the power if $V = 12 \, V$ and $I = 0.5 \, A$.

   $P = 6 \, W$. Using $P = VI = 12 \times 0.5 = 6$ W.

3. Identify the formula for power loss in terms of voltage drop and current.

   $P_{\text{loss}} = I \cdot \Delta V$. Power loss equals current times voltage drop.

4. Convert $10 \, \text{kW}$ to watts.

   $10,000 \, W$. $1$ kW $= 1000$ W, so $10$ kW $= 10,000$ W.

5. What is the role of a transformer in power transmission?

   Adjusts voltage levels. Transformers step voltage up or down efficiently.

6. What is the power dissipation if $V = 10 \, V$ and $R = 5 \, \text{Ω}$?

   $P = 20 \, W$. Using $P = \frac{V^2}{R} = \frac{10^2}{5} = 20$ W.

7. What is the power output if $E = 500 \, \text{J}$ and $t = 10 \, \text{s}$?

   $P = 50 \, W$. Using $P = \frac{E}{t} = \frac{500}{10} = 50$ W.

8. What is the unit of reactive power?

   Volt-ampere reactive (VAR). VAR is the unit for reactive power.

9. Calculate power if $V = 120 \, V$, $I = 3 \, A$, and $\cos \phi = 0.9$.

   $P = 324 \, W$. Using $P = VI\cos\phi = 120 \times 3 \times 0.9 = 324$ W.

10. State the expression for power factor in terms of real and apparent power.

    $\text{Power Factor} = \frac{P}{S}$. Power factor equals real power over apparent power.

11. What is the formula for electric power in terms of voltage and resistance?

    $P = \frac{V^2}{R}$. Power equals voltage squared divided by resistance.

12. What is the resistance if $P = 60 \, W$ and $I = 2 \, A$?

    $R = 15 \, \text{Ω}$. Using $P = I^2R$, so $R = \frac{P}{I^2} = \frac{60}{4} = 15$ Ω.

13. What is the formula for electric power in terms of current and voltage?

    $P = IV$. Power is the product of voltage and current.

14. Calculate the energy consumed in $2 \, \text{hours}$ by a $100 \, W$ bulb.

    $E = 0.2 \, \text{kWh}$. Using $E = Pt = 0.1 \times 2 = 0.2$ kWh.

15. What unit is used to measure apparent power?

    Volt-ampere (VA). VA measures the magnitude of AC power.

16. State the relationship between power, energy, and time.

    $P = \frac{E}{t}$. Power is energy divided by time.

17. What does $1 \, \text{kWh}$ represent in terms of energy?

    $3.6 \times 10^6 \, \text{J}$. One kWh equals 3.6 million joules.

18. Define the term 'active power' in AC circuits.

    Real power. Active power performs actual work in circuits.

19. What is the rate of energy transfer called in an electrical circuit?

    Electric Power. Power is energy transferred per unit time.

20. Find the power factor if the power is $400 \, W$, $I = 5 \, A$, and $V = 100 \, V$.

    $\cos \phi = 0.8$. Power factor = $\frac{P}{VI} = \frac{400}{5 \times 100} = 0.8$.

21. State the formula for electric power in terms of resistance and current.

    $P = I^2R$. Power equals current squared times resistance.

22. Which physical quantity is measured in kilowatt-hours?

    Energy. kWh measures energy consumption over time.

23. Identify the formula for efficiency in terms of power.

    $\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100\%$. Efficiency is output power divided by input power.

24. Identify the unit of energy used in electric bills.

    Kilowatt-hour (kWh). kWh is the commercial unit for electrical energy.

25. What is the efficiency if $P_{\text{out}} = 90 \, W$ and $P_{\text{in}} = 100 \, W$?

    $\eta = 90\%$. Efficiency = $\frac{90}{100} \times 100\% = 90\%$.

26. What is the significance of reactive power in AC circuits?

    Non-working power. Reactive power doesn't perform useful work.

27. Calculate the apparent power if $V = 220 \, V$ and $I = 5 \, A$.

    $S = 1100 \, VA$. Using $S = VI = 220 \times 5 = 1100$ VA.

28. Define apparent power in an AC circuit.

    $S = VI$. Apparent power is the total power in AC circuits.

29. How is reactive power denoted in an electrical circuit?

    $Q$. $Q$ represents reactive power in circuits.

30. What is the phase angle for a purely resistive circuit?

    $0^\circ$. Resistive circuits have zero phase difference.

31. Calculate the power if $I = 2 \, A$ and $V = 5 \, V$.

    $P = 10 \, W$. Using $P = IV = 2 \times 5 = 10$ W.

32. Identify the unit of electric power in the International System of Units.

    Watt (W). The SI unit for power is the watt.

33. State the formula for instantaneous power in terms of time.

    $p(t) = v(t) \cdot i(t)$. Instantaneous power is voltage times current.

34. What is the power loss in a transmission line given $I = 10 \, A$ and $R = 2 \, \text{Ω}$?

    $P_{\text{loss}} = 200 \, W$. Using $P_{\text{loss}} = I^2R = 10^2 \times 2 = 200$ W.

35. What does a power factor of 1 signify in an AC circuit?

    Purely resistive load. Unit power factor means no reactive components.

36. Determine the power consumed by a $4 \, \text{Ω}$ resistor with $3 \, A$ current.

    $P = 36 \, W$. Using $P = I^2R = 3^2 \times 4 = 36$ W.

37. Find the power factor if apparent power is $1000 \, VA$ and real power is $800 \, W$.

    $\cos \phi = 0.8$. Power factor = $\frac{P}{S} = \frac{800}{1000} = 0.8$.

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