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QPages 352-354: Q20: HC Verma: Concepts of Physics - Volume 2 Electric Current through Gases Pages 352-354: Q20 Solution: The plate current in a triode can be written as . Show that the …

⚠️ Common Exam Traps & Conceptual Pitfalls

When differentiating the plate current equation $i_p \propto (V_g + V_p/\mu)^{3/2}$ with respect to $V_g$, students often forget to reduce the exponent by 1, incorrectly keeping it as $3/2$ instead of $1/2$. This error prevents the correct substitution of the voltage term back in terms of $i_p$, leading to a false proportionality of $i_p^{1/2}$ instead of the required $i_p^{1/3}$.

The plate current in a triode can be written as

i_p = kV_g + V_p/\mu)^{3/2}

. Show that the mutual conductance is proportional to the cube root of the plate current.

Step-by-Step Verified Solution

**Answer:**

g_m \propto i_p^{1/3}

. **Step-by-Step Explanation:** Given:

i_p = k(V_g + V_p/\mu)^{3/2}

.

g_m = \frac{\partial i_p}{\partial V_g} = k \times \frac{3}{2}\left(V_g + \frac{V_p}{\mu}\right)^{1/2}

From the original equation:

\left(V_g + \frac{V_p}{\mu}\right) = \left(\frac{i_p}{k}\right)^{2/3}

.

g_m = \frac{3k}{2} \left(\frac{i_p}{k}\right)^{1/3} = \frac{3k^{2/3}}{2} i_p^{1/3} \propto i_p^{1/3}

All Questions in this Chapter

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