Decode the resistor color code

The bands are: green, black, red, brown.

For a 4-band resistor:

• 1st band = first digit
• 2nd band = second digit
• 3rd band = multiplier
• 4th band = tolerance

Using standard color codes:

• Green $= 5$
• Black $= 0$
• Red $= 10^2$
• Brown $= \pm 1\%$

So the resistance is $R = 50 \times 10^2 = 5000\ \Omega = 5\,\text{k}\Omega$

Use the power rating

The resistor is rated at $2\,\text{W}$, so the maximum safe power is $P_{\max} = 2\,\text{W}$

For a resistor, $P = I^2 R$

Hence the maximum current is $I_{\max} = \sqrt{\frac{P_{\max}}{R}}$

Substitute the values

$I_{\max} = \sqrt{\frac{2}{5000}}$

$I_{\max} = \sqrt{4 \times 10^{-4}}$

$I_{\max} = 2 \times 10^{-2}\,\text{A} = 0.02\,\text{A}$

$I_{\max} = 20\,\text{mA}$

Match with the options

• A: $0.4\,\text{mA}$
• B: $20\,\text{mA}$
• C: $63\,\text{mA}$
• D: $100\,\text{mA}$

Therefore, the correct option is: $\boxed{\text{B: }20\,\text{mA}}$

Comparison with stored correct answer

Stored correct answer = B

My derived answer = B

So they agree.