The figure shows variation of the current through the heating element with time in an iron when it is plugged into a standard 120 V, 60 Hz outlet.
-What is the resistance of the iron?
A)24 $\varOmega$
B)7.1 $\varOmega$
C)17 $\varOmega$
D)12 $\varOmega$
E)1.8 $\varOmega$

Question

The figure shows variation of the current through the heating element with time in an iron when it is plugged into a standard 120 V, 60 Hz outlet. 
-What is the resistance of the iron?
A)24 $\varOmega$ 
B)7.1 $\varOmega$ 
C)17 $\varOmega$ 
D)12 $\varOmega$ 
E)1.8 $\varOmega$

Quizplus · Accepted Answer

According to Ohm's law, V = IR, where V is the voltage, I is the current, and R is the resistance. From the graph, we can see that the current peaks at about 10 amps. At this point, the voltage is 120 V. Therefore, the resistance of the iron can be calculated as R = V / I = 120 V / 10 A = 12 Ω. However, this only gives us the resistance at the peak current, and the resistance will vary as the current varies. To get an average resistance, we can use the formula Ravg = Vrms / Irms, where Vrms and Irms are the root mean square (RMS) values of the voltage and current, respectively. For a standard 120 V, 60 Hz outlet, the RMS voltage is Vrms = V / sqrt(2) = 84.85 V. To find the RMS current, we need to calculate the area under the curve of the current vs. time graph and divide by the time period. This gives us Irms = 7 amps. Therefore, the average resistance is Ravg = Vrms / Irms = 84.85 V / 7 A = 12.12 Ω. This is still only an approximation, but it is closer to the actual value. Since none of the answer choices match exactly, the closest one is C) 17 Ω.

The Figure Shows Variation of the Current Through the Heating Ω\varOmegaΩ

The Figure Shows Variation of the Current Through the Heating $\varOmega$