Calculating input voltage via cascaded transformer ratios

Steps:

• From the diagram, the lamp operates at 6V output from the second transformer.
• The second transformer has a 1:1 turns ratio, so its primary (output from first transformer) is also 6V.
• The first transformer has a 2:1 turns ratio (Np:Ns), stepping down voltage.
• Apply the transformer formula Vp = Vs × (Np/Ns) = 6V × 2 = 12V for the input to the primary.

Why C is correct:

• 12V satisfies the turns ratio formula Vp/Vs = Np/Ns, ensuring 6V at the lamp for proper operation.

Why the others are wrong:

• A: 0.12V is far too low, yielding ~0.06V output, insufficient to light the lamp.
• B: 6V gives 3V output, dimming the lamp below rated brightness.
• D: 9V produces 4.5V output, still underpowering the lamp.

Final answer: C