Circuit Analysis:

• Let node $B$ be at reference potential $V_B = 0\,\text{V}$.
• The battery maintains the top wire at $24\,\text{V}$.
• The junction between the two vertical $8\,\text{k}\Omega$ resistors is at a positive potential relative to $B$.
• Because the p-side (anode) of the diode is connected to this positive junction and the n-side (cathode) connects to node $A$ (which is connected to $0\,\text{V}$ via the right $8\,\text{k}\Omega$ resistor), the diode is FORWARD BIASED.
• Assuming an ideal diode, it acts as a short circuit with zero resistance.
  6. Consequently, the right branch $8\,\text{k}\Omega$ resistor is connected in parallel with the bottom $8\,\text{k}\Omega$ resistor across terminals $A$ and $B$:
  $$R_{\text{parallel}} = \frac{8\,\text{k}\Omega \times 8\,\text{k}\Omega}{8\,\text{k}\Omega + 8\,\text{k}\Omega} = 4\,\text{k}\Omega$$
  7. The total equivalent circuit resistance is:
  $$R_{\text{total}} = 8\,\text{k}\Omega + R_{\text{parallel}} = 8 + 4 = 12\,\text{k}\Omega$$
  8. Using the voltage divider rule, the potential across the parallel combination (between $A$ and $B$) is:
  $$V_{AB} = 24\,\text{V} \times \frac{4\,\text{k}\Omega}{12\,\text{k}\Omega} = 24 \times \frac{1}{3} = 8\,\text{V}$$

The maximum line-of-sight distance $d$ up to which a TV signal transmitted from a tower of height $h$ can be received on Earth (radius $R$) is:

$$d = \sqrt{2 R h}$$

Given:

• $h = 180\,\text{m}$
• $R = 6.4 \times 10^6\,\text{m}$

Calculating $d$:

$$d = \sqrt{2 \times (6.4 \times 10^6) \times 180}$$ $$d = \sqrt{2304 \times 10^6} = \sqrt{2304} \times 10^3 = 48 \times 10^3\,\text{m} = 48\,\text{km}$$

Matching definitions in communication systems:

• Modulation: The process of superimposing a low-frequency information signal onto a high-frequency carrier wave for long-distance transmission (Matches III).
• Baseband signals: The band of original frequencies representing the raw information without modulation (Matches IV).
• Demodulation: The process of recovering the original information signal from the modulated carrier wave at the receiver (Matches I).
• Bandwidth: The range of frequencies over which an electronic transmission equipment operates or accommodates signals (Matches II).

Correct match: A-III, B-IV, C-I, D-II.