When a 14.0-A current flows through an 8.00-Ω device for 24.0 hours, how much does this cost if energy costs $0.0900 per kW · h?
A) $\$ 0.24$
B) $\$ 2.16$
C) $\$ 3.39$
D) $\$ 1.04$

Question

When a 14.0-A current flows through an 8.00-Ω device for 24.0 hours, how much does this cost if energy costs $0.0900 per kW · h? 
A) $\$ 0.24$
B) $\$ 2.16$
C) $\$ 3.39$
D) $\$ 1.04$

Quizplus · Accepted Answer

First, calculate the energy used in kilowatt-hours (kWh). Power (P) is given by $P = IV$, where $I$ is current and $V$ is voltage. Ohm's law states $V = IR$, so $P = I^2R$. Given $I = 14.0 \, \text{A}$ and $R = 8.00 \, \Omega$, $P = (14.0)^2 \times 8.00 = 1568 \, \text{W} = 1.568 \, \text{kW}$. The energy used over 24.0 hours is $E = P \times t = 1.568 \, \text{kW} \times 24.0 \, \text{h} = 37.632 \, \text{kWh}$. At $0.0900 per kWh, the cost is $37.632 \, \text{kWh} \times \$0.0900/\text{kWh} = \$3.39$.

When a 140-A Current Flows Through an 8 $0.24\$ 0.24$0.24 B) $2.16\$ 2.16$2.16

When a 140-A Current Flows Through an 8 $\$ 0.24$ B) $\$ 2.16$