Voltage divider circuit analysis

Steps:

• The circuit is a series combination of 12 V supply, 150 Ω resistor, and thermistor T; 4.5 V is across the resistor.
• Current I = voltage across resistor / resistance = 4.5 V / 150 Ω = 0.03 A.
• Voltage across thermistor = total voltage - voltage across resistor = 12 V - 4.5 V = 7.5 V.
• Resistance of T = voltage across T / I = 7.5 V / 0.03 A = 250 Ω.

Why C is correct:

• Option C (250 Ω) matches the calculation from Ohm's law: R = V/I for the thermistor branch.

Why the others are wrong:

• A: 90 Ω assumes 4.5 V across T, inverting the voltage drop.
• B: 150 Ω equals the fixed resistor, ignoring voltage division.
• D: 400 Ω would drop 9 V across T at equal current, exceeding total supply.

Final answer: C