Task Sets: Electric Power - OpenStax Physics (High School)

A

Recall / Warm-Up

1.

In mechanics, power is defined as the rate of doing work. Which expression correctly states this definition?

A.

$P = \frac{W}{t}$

B.

$P = W \cdot t$

C.

$P = \frac{t}{W}$

D.

$P = \frac{F}{d}$

2.

A circuit element has a potential difference of $V$ across it and a current $I$ flowing through it. Which expression gives the power delivered to the element?

A.

$P = V + I$

B.

$P = \frac{V}{I}$

C.

$P = IV$

D.

$P = \frac{I}{V}$

3.

Ohm's Law states the relationship between voltage, current, and resistance in a resistor. Which equation is correct?

A.

$V = I \cdot R$

B.

$V = \frac{R}{I}$

C.

$I = V \cdot R$

D.

$R = V \cdot I$

B

Fluency Practice

1.

A hair dryer operates at $120\ \text{V}$ and draws a current of $12.5\ \text{A}$ . Calculate the power consumed by the hair dryer in watts.

2.

A $60\ \text{W}$ light bulb operates at $120\ \text{V}$ . What current flows through the bulb? Give your answer in amperes.

3.

A resistor has resistance $R = 40\ \Omega$ and carries a current of $3\ \text{A}$ . Calculate the power dissipated in the resistor using the formula $P = I^2R$ .

Decision tree showing which power formula to use: P=IV when given I and V, P=I-squared-R when given I and R, P=V-squared-over-R when given V and R, with the V and R row highlighted

4.

A resistor has $V = 24\ \text{V}$ across it and $R = 8\ \Omega$ . Which formula should you use to calculate power directly from these two values, and what is the result?

A.

$P = IV$ ; find $I$ first: result is $72\ \text{W}$

B.

$P = I^2R$ ; result is $72\ \text{W}$

C.

$P = V^2/R$ ; result is $72\ \text{W}$

D.

$P = V^2/R$ ; result is $576\ \text{W}$

5.

An electric heater has resistance $R = 20\ \Omega$ and is connected to a $240\ \text{V}$ outlet. Calculate the power dissipated using $P = V^2/R$ .

6.

A $150\ \text{W}$ refrigerator runs for $8\ \text{hours}$ . How many kilowatt-hours of energy does it use?

C

Varied Practice

D

Word Problems

1.

A phone charger is rated at 5 W and is left plugged in for 8 hours per day. Electricity costs 0.15 dollars per kWh.

How much does it cost in dollars to charge the phone for one day? Round to the nearest cent.

2.

A household runs these appliances daily: a refrigerator (150 W, 24 h/day), a television (100 W, 4 h/day), and an air conditioner (1500 W, 6 h/day). Electricity costs 0.15 dollars per kWh.

1.

Calculate the total daily energy consumption of all three appliances in kWh.

2.

Calculate the daily electricity cost in dollars for the air conditioner alone.

3.

A power plant generates $P = 500\ \text{kW}$ and transmits it over a line with total resistance $R_\text{line} = 5\ \Omega$ . The transmission voltage is $50{,}000\ \text{V}$ .

Calculate the power lost in the transmission line in watts.

E

Error Analysis

1.

A student wrote: "A 100 W incandescent bulb is better than a 15 W LED because it has more power — power means capability, so more watts means more light output."

What is the fundamental error in this reasoning?

A.

Watts measure the rate of energy conversion, not efficiency or useful output. Higher wattage means more energy used, not necessarily more useful output.

B.

The student used the wrong formula — they should have compared V and I instead of wattage.

C.

There is no error — a higher wattage bulb always produces more light.

D.

The error is that comparing two different types of bulbs is not valid.

2.

A student explained power transmission this way: "Power companies use high voltage because Ohm's Law says I = V/R. So higher voltage means more current through the line, and more current means more power delivered."

Identify and correct the error in this explanation.

A.

The error is applying Ohm's Law at all — Ohm's Law does not apply to transmission lines.

B.

The student has the relationship backwards. The goal is to transmit fixed power P = IV. Higher V means lower I, which reduces I²R losses in the line.

C.

The student is correct — higher voltage does produce more current, and more current does deliver more power.

D.

The error is that Ohm's Law gives $V = IR$ , not $I = V/R$ — these are different formulas.

F

Challenge / Extension

1.

A power plant generates $P = 2\ \text{MW}$ at $20{,}000\ \text{V}$ . A step-up transformer raises the voltage to $400{,}000\ \text{V}$ for transmission. The transmission line has resistance $R_\text{line} = 8\ \Omega$ .

What percentage of the generated power is lost in the transmission line? Round to two decimal places.

2.