Question

A $2W$ carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is :

• A. $0.4mA$
• B. $20mA$
• C. $63mA$
• D. $100mA$

Answer 1

The correct option is B

$20mA$

Step 1: Given data

Power of the carbon resistor, $P=2W$

Color coding is green, black, red and brown respectively.

Step 2: Explain color coding

Color	Value	Multiplier	Tolerance
Green	$5$	$\times {10}^5$	$\pm 0.5\%$
Black	$0$	$\times {10}^0$	$\pm 20\%$
Red	$2$	$\times {10}^2$	$\pm 2\%$
Brown	$1$	$\times {10}^1$	$\pm 1\%$

Step 3: Find out the value of resistance according to the color coding

From color coding, $R=50\times {10}^{2}ohm$

Step 4: Calculate the maximum current

Power of the resistor, $P={\left(i_{max}\right)}^2\times R$

$$\begin{gathered} 20W={\left(i_{max}\right)}^2\times 50\times {10}^{2}ohm \\ {\left(i_{max}\right)}^2=20/\left(50\times {10}^2\right) \\ {i}_{max}=20\times {10}^{-3}A \\ {i}_{max}=20mA \end{gathered}$$

Hence, option (B) is correct.