If the current in the circuit for heating the filament is increased, the cutoff wavelength

Options

A. will increase
B. will decrease
C. will remain unchanged
D. will change

Answer

To solve the question regarding the effect of increasing the current in the circuit for heating the filament on the cutoff wavelength, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The cutoff wavelength (λ_min) is related to the energy of the emitted photons, which can be expressed using the equation:
\[ \frac{hc}{\lambda_{\text{min}}} = eV \]
where:
- \(h\) is Planck's constant,
- \(c\) is the speed of light,
- \(e\) is the charge of an electron,
- \(V\) is the potential difference applied.

2. **Rearranging the Equation**: From the above equation, we can rearrange it to express λ_min:
\[ \lambda_{\text{min}} = \frac{hc}{eV} \]
This shows that the cutoff wavelength is inversely proportional to the potential difference \(V\).

3. **Analyzing the Effect of Current**: The question states that the current in the circuit for heating the filament is increased. However, the cutoff wavelength depends only on the potential difference \(V\) and not directly on the current.

4. **Conclusion**: Since the current affects the heating of the filament and can influence the temperature, it does not directly affect the potential difference \(V\) applied in the context of the cutoff wavelength. Therefore, if the potential difference remains unchanged, the cutoff wavelength will also remain unchanged.

5. **Final Answer**: The cutoff wavelength will remain unchanged when the current in the circuit for heating the filament is increased. Thus, the correct option is **Option 3**.