Final answer:
The input current required to produce a 12 V output at 200 mA is calculated to be 20 mA. Considering a power input of 2.4 W, this amount of power is reasonable for a small appliance.
Step-by-step explanation:
The question pertains to the use of a plug-in transformer to reduce the mains voltage of 120V AC to a lower voltage for electronic devices such as cassette recorders, which are designed to operate at 12 V.
The cassette recorder's transformer has a maximum current output of 200 mA (0.2 A).
To calculate the required current input, we apply the principle of conservation of energy, assuming the transformer is 100% efficient (power input equals power output).
Calculation for Current Input:
Power output = Voltage output x Current output
= 12 V x 0.2 A
= 2.4 W
Power input = Power output (assuming 100% efficiency)
Current input = Power input / Voltage input
Current input = 2.4 W / 120 V
= 0.02 A or 20 mA
Calculation for Power Input:
Power input = Voltage input x Current input
= 120V x 0.02 A
= 2.4 W
Reasonableness of Power for a Small Appliance
A power input of 2.4 W is quite reasonable for a small appliance like a cassette recorder. It draws a low current and consumes a moderate amount of power, typical of small, portable electronic devices.
Hence, a power input of 2.4 W is quite reasonable for a small appliance like a cassette recorder.