Final answer:
The current input of a transformer that converts 120 V to 12.0 V with a maximum output current of 200 mA is 0.02 A or 20 mA, assuming 100% efficiency. The power input and output are both 2.4 W, which is reasonable for a small appliance. None of the options provided is correct.
Step-by-step explanation:
Transformer Current and Power Calculations
A cassette recorder uses a plug-in transformer to convert 120 V to 12.0 V, with a maximum current output of 200 mA. To find the current input of a transformer, we can use the conservation of power principle (assuming 100% efficiency), which states that the power input (Pinput) equals the power output (Poutput). The power output can be calculated by multiplying the output voltage (V output) by the output current (I output).
First, convert 200 mA to amperes: 200 mA = 0.2 A. Then calculate the power output:
(12.0 V) × (0.2 A) = 2.4 W.
Since the power output must equal the power input, and the input voltage is 120 V, we can calculate the current input (Iinput) by rearranging the power input formula P = VI:
Iinput = Pinput / Vinput = 2.4 W / 120 V = 0.02 A or 20 mA.