The coil of a heater is cut into two cqual halves and only one of them is used in the heater. The ratio of the heat produced by this half of the coil to that produced by the original coil is

Options

A. `2:1`
B. `4:1`
C. `1:2`
D. `1:4`

Explanation

To solve the problem of finding the ratio of the heat produced by half of the coil to that produced by the original coil, we can follow these steps:

### Step 1: Understand the Resistance of the Coil
Let the total resistance of the original coil be \( R \). When the coil is cut into two equal halves, the resistance of each half becomes:
\[ R_1 = R_2 = \frac{R}{2} \]

### Step 2: Use the Formula for Heat Produced
The heat produced by a resistor is given by the formula:
\[ H = I^2 R t \]
However, since the current \( I \) depends on the voltage \( V \) and resistance \( R \) (Ohm's Law: \( I = \frac{V}{R} \)), we can express heat in terms of voltage:
\[ H = \frac{V^2}{R} t \]

### Step 3: Calculate Heat Produced by Half the Coil
For the half coil (with resistance \( \frac{R}{2} \)):
\[ H_1 = \frac{V^2}{\frac{R}{2}} t = \frac{2V^2}{R} t \]

### Step 4: Calculate Heat Produced by the Original Coil
For the original coil (with resistance \( R \)):
\[ H_2 = \frac{V^2}{R} t \]

### Step 5: Find the Ratio of Heat Produced
Now, we can find the ratio of the heat produced by the half coil to that produced by the original coil:
\[ \frac{H_1}{H_2} = \frac{\frac{2V^2}{R} t}{\frac{V^2}{R} t} = \frac{2V^2}{R} \cdot \frac{R}{V^2} = 2 \]

### Conclusion
Thus, the ratio of the heat produced by the half coil to that produced by the original coil is:
\[ \text{Ratio} = 2:1 \]