Two discharge tubes have identical mater...

Two discharge tubes have identical material structure and the same gas is filled in them. The length of one tube is 10cm and that of th other tube is 20cm. 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?

Text Solution

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`V = f(Pd), v_8 =P_8 d_8, v_L = P_l d_l `
` V_s/V_l = P_s/P_l xx d_s/d_l `
` rArr 100/100 = 10/20 xx 1mm/x `
` rArr 20/10 = 1mm/x `
` rArr x = 1mm/2 = 0.5mm ` .

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