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The voltmeter shown in figure reads 18V ...

The voltmeter shown in figure reads 18V across the `50(Omega)`resistor. Find the resistance of the voltmeter.

Text Solution

Verified by Experts

Let resistance of the voltameter be `R Omega`
` R_1 = 50R/50+R `
` R_2 = 24 Omega `
` Both are in series `
` 30 = V_1 + V_2 `
` rArr 30 = iR_1 + iR_2 `
` rArr iR_1 = 30 - (30/(R_1+R_2)) R_2`
` V_1 = 30 (1- (R_2/(R_1 + R_2))`
` V_1 = 30 ((R_1 + R_2+R_2)/(R_1)+(R_2)) `
` V_1 = 30(R_1 / R_1 + R_2) `
` 18 = 30 (50 R / (50+R)[50R/(50 + R) +24]) `
` = 30 [50R/(50R + 24(50+R))]`
` 18 = (30 xx 50 xx R / 74 R + 1200 ) `
` R = 130 Omega ` .
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