A 2W carbon resistor is colour-coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is (A) 63mA(B) 0.4mA(C) 100mA(D) 20mA

To determine the maximum current that can be passed through a resistor, we need to use the power rating of the resistor and Ohm's law.
Step 1: Determine the resistance value
The color code of the resistor is given as green, black, red, and brown. The color code works as follows:
• Green: 5
• Black: 0
• Red: Multiplier of 102=10010^2 = 100
• Brown: Tolerance (±1%), but we don’t need this for now.
So, the value of the resistance is:
Resistance=50×100=5000 Ω=5 kΩ\text{Resistance} = 50 \times 100 = 5000 \, \Omega = 5 \, \text{k}\Omega
Step 2: Use the power formula
The maximum power PP that the resistor can handle is 2W, and we can use the formula for power:
P=I2RP = I^2 R
Where:
• PP is the power (2 W),
• II is the current (which we need to find),
• RR is the resistance (5000 ohms).
Rearranging the formula to solve for current II:
I=PR=25000=0.0004=0.02 A=20 mAI = \sqrt{\frac{P}{R}} = \sqrt{\frac{2}{5000}} = \sqrt{0.0004} = 0.02 \, \text{A} = 20 \, \text{mA}
Step 3: Conclusion
The maximum current that can be passed through this resistor is 20 mA.
Thus, the correct answer is:
D.20mA\boxed{D. 20mA}