Electronics (ECE) - MCQ Practice Questions

Understanding:

We must find the intrinsic impedance of a lossless dielectric medium.

Formula:

The intrinsic impedance of a lossless medium is:

Step 1: Substitute values

Answer:

The intrinsic impedance of the medium is approximately $125.7\Omega$.

Quick Tip:

With ${\mu }_r=1$, higher ${\epsilon }_r$ always lowers $\eta$ below ${\eta }_0$. The speed of light in this medium is also reduced by $\sqrt{{\epsilon }_r{\mu }_r}=3$, giving $v=c/3$.

Understanding:

We need to find the $x$-component of $\mathbf{E}$ from the given scalar potential $V$.

Formula:

The electric field is the negative gradient of the potential:

Step 1: Compute partial derivatives

Step 2: Evaluate $E_x$ at $(1,2,3)$

Answer:

The $x$-component of the electric field at $(1,2,3)$ is $-6\text{V/m}$.

Quick Tip:

The negative sign in $\mathbf{E}=-\nabla V$ is frequently dropped by mistake, giving $+6\text{V/m}$. Always remember that $\mathbf{E}$ points in the direction of decreasing potential.