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QPages 352-354: Q4: HC Verma: Concepts of Physics - Volume 2 Electric Current through Gases Pages 352-354: Q4 Solution: Two discharge tubes have identical material structures and the…

Two discharge tubes have identical material structures and the same gas is filled in them. The length of one tube is 10 cm and that of the other tube is 20 cm. Sparking starts in both the tubes when the potential difference between the cathode and the anode is 100 V. If the pressure in the shorter tube is 1.0 mm of mercury, what is the pressure in the longer tube?

Step-by-Step Verified Solution

**Answer:** The pressure in the longer tube is 0.5 mm of mercury. **Step-by-Step Explanation:** Sparking condition depends on the product PdPd (Paschen's law). Since sparking occurs at the same potential difference for both tubes, P1d1=P2d2P_1 d_1 = P_2 d_2. Given: P1=1.0P_1 = 1.0 mm Hg, d1=10d_1 = 10 cm, d2=20d_2 = 20 cm. P2=P1d1d2=1.0×1020=0.5P_2 = P_1 \frac{d_1}{d_2} = 1.0 \times \frac{10}{20} = 0.5 mm Hg .

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