The order of coloured rings in a carbon resistor is red, yellow, blue and silver. The resistance of the carbon resistor is

Options

A. `24 xx 10^(6) Omega +- 5%`
B. `24 xx 10^(6) Omega +- 10%`
C. `34 xx 10^(4) Omega +- 10%`
D. `26 xx 10^(4) Omega +- 5%`

Answer

To determine the resistance of the carbon resistor with the color bands red, yellow, blue, and silver, we will follow these steps:

### Step 1: Identify the color codes
- The first band (Red) corresponds to the number 2.
- The second band (Yellow) corresponds to the number 4.
- The third band (Blue) indicates the multiplier, which is \(10^6\).
- The fourth band (Silver) indicates the tolerance, which is ±10%.

### Step 2: Combine the first two bands
The first two bands represent the significant figures of the resistance value. Therefore, we combine the numbers from the first two bands:
- First band (Red) = 2
- Second band (Yellow) = 4

So, combining these gives us:
\[ 24 \]

### Step 3: Apply the multiplier
The third band (Blue) indicates the multiplier, which is \(10^6\). Therefore, we multiply the significant figure by the multiplier:
\[ 24 \times 10^6 = 24,000,000 \, \text{ohms} \]

### Step 4: Include the tolerance
The fourth band (Silver) indicates a tolerance of ±10%. This means the actual resistance can vary by 10% above or below the calculated value:
- 10% of \(24,000,000\) ohms is:
\[ 0.10 \times 24,000,000 = 2,400,000 \, \text{ohms} \]

### Step 5: State the final resistance value with tolerance
Thus, the resistance of the carbon resistor is:
\[ 24,000,000 \, \text{ohms} \pm 2,400,000 \, \text{ohms} \]

### Final Answer
The resistance of the carbon resistor is \(24,000,000 \, \text{ohms} \, (24 \, M\Omega) \) with a tolerance of ±10%.

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