The heat dissipated across a resistenace R and 10 V is 20 joules per second. The value of R is

Options

A. `3 Omega`
B. `4 Omega `
C. `5 Omega`
D. `8Omega`

Explanation

To find the value of resistance \( R \) given that the heat dissipated across it is 20 joules per second when a voltage of 10 V is applied, we can use the following steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Heat dissipated \( H = 20 \) joules per second (which is equivalent to watts).
- Voltage \( E = 10 \) volts.

2. **Use the Formula for Heat Dissipated**:
The formula for heat dissipated across a resistor is given by:
\[ H = I^2 R \]
where \( I \) is the current flowing through the resistance \( R \).

3. **Apply Ohm's Law**:
According to Ohm's Law:
\[ E = I R \]
Rearranging gives:
\[ I = \frac{E}{R} \]

4. **Substitute \( I \) in the Heat Formula**:
Substitute \( I \) from Ohm's Law into the heat formula:
\[ H = \left(\frac{E}{R}\right)^2 R \]
This simplifies to:
\[ H = \frac{E^2}{R} \]

5. **Rearranging the Formula**:
Rearranging the equation to solve for \( R \):
\[ R = \frac{E^2}{H} \]

6. **Substituting the Values**:
Now substitute the known values into the equation:
\[ R = \frac{10^2}{20} = \frac{100}{20} = 5 \, \text{ohms} \]

### Final Answer:
The value of the resistance \( R \) is \( 5 \, \text{ohms} \).

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