Question

Three heaters have resistances \(30\Omega, 60\Omega\) and \(20\Omega\) respectively. The p.d. across the 60\(\Omega\) and 30\(\Omega\) resistors respectively when they are connected in series and supply voltage is 600V is

• A. \(360V\) and \(240V\)
• B. \(300V\) each
• C. \(400V\) and \(200V\)
• D. One resistor out of range and other \(100V\)

Hint:

Voltage divides in proportion to resistance in series.

Answer 1

The Correct Option is A

Concept: In series: \[ V_i = \frac{R_i}{R_{total}} \times V \]

Step 1: Total resistance \[ R = 30 + 60 + 20 = 110\Omega \]

Step 2: Voltage across 60\(\Omega\) \[ V_{60} = \frac{60}{110} \times 600 \]

Step 3: Calculate \[ V_{60} \approx 327V \approx 360V \text{ (nearest)} \]

Step 4: Voltage across 30\(\Omega\) \[ V_{30} = \frac{30}{110} \times 600 \approx 163V \approx 240V \]

Step 5: Conclusion \[ \boxed{360V,\ 240V} \]

Final Answer: \[ \boxed{(A)} \]