Two conductors with resistance Rand 2R respectively connected to a de source. Ratio of their heat will be:

Options

A. `1:1`
B. `2:1`
C. `1:2`
D. `2:2`

Explanation

To solve the problem of finding the ratio of heat produced in two conductors with resistances \( R \) and \( 2R \) connected to a DC source, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Let the resistance of the first conductor be \( R_1 = R \).
- Let the resistance of the second conductor be \( R_2 = 2R \).
- Both conductors are connected to the same voltage source \( V \).

2. **Use the Formula for Heat Produced:**
The heat produced in a resistor when a current flows through it can be calculated using the formula:
\[ Q = \frac{V^2}{R} \cdot t \]
where \( Q \) is the heat produced, \( V \) is the voltage across the resistor, \( R \) is the resistance, and \( t \) is the time for which the current flows.

3. **Calculate Heat for Each Conductor:**
- For the first conductor (resistance \( R_1 \)):
\[ Q_1 = \frac{V^2}{R_1} \cdot t = \frac{V^2}{R} \cdot t \]
- For the second conductor (resistance \( R_2 \)):
\[ Q_2 = \frac{V^2}{R_2} \cdot t = \frac{V^2}{2R} \cdot t \]

4. **Find the Ratio of Heat Produced:**
To find the ratio of the heat produced in the two conductors, we take:
\[ \frac{Q_1}{Q_2} = \frac{\frac{V^2}{R} \cdot t}{\frac{V^2}{2R} \cdot t} \]
The \( V^2 \) and \( t \) terms cancel out:
\[ \frac{Q_1}{Q_2} = \frac{1/R}{1/(2R)} = \frac{2R}{R} = 2 \]

5. **Conclusion:**
Therefore, the ratio of heat produced in the first conductor to the second conductor is:
\[ \frac{Q_1}{Q_2} = 2:1 \]

### Final Answer:
The ratio of heat produced in the two conductors is \( 2:1 \).