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In the circuit shows in Fig. 6.22, a vol...

In the circuit shows in Fig. `6.22`, a voltmeter reads `30 V` when it is connected across a `400 omega` resistance. Calculate what the same voltmeter would read when it is connected across the `300 Omega` resistance.

Text Solution

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Let the resistance of the voltmeter be `R_(V)` and the current flowing through it be `I_(V)`.

Then `I_(V) R_(V) = 30` and `(I - I_(V)) xx 400 = 30`
Also, `300 xx I = 30` or `I = 0.1 A`
Therefore, `0.1 - I_(V) = 3//40`
or `I_(V) = 0.1 -(3)/(40) = (4 - 3)/(40) = (1)/(40) A`
`:. (1)/(40) xx R_(V) = 30` or `R_(V) = 1200 Omega`

For the circuit in Fig. `S6.7`,
`I_(V) xx R_(V) = (I - I_(V)) 300` or `I_(V) xx 1200 = (I - I_(V)) 300`
or `4I_(V) = I - I_(V)` or `I = 5I_(V)` (i)
Also, `300 (I - I_(V)) + 400 I = 60` or `700 I - 300 I_(V) = 60`
`3500 I_(V) - 300 I_(V) = 60` or `I_(V) = (60)/(3200) = (3)/(160) A`
Therefore, reading of voltmeter is `(3)/(160) xx 1200 = 22.5 V`
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