In the circuit given below, a voltmeter reads `20V` when it is connected across `400Omega` resistance. Calculate what the same voltmeter will read when connected across the `200Omega` resistance.

Options

A. `100V`
B. `50V`
C. `30V`
D. `10V`

Explanation

Let G be the resistance of voltmeter connected in parallel to `400Omega` resistance. Net resistance
`R_P=(400G)/(400+G)`
Now, Resistance `200Omega` and `R_P` are in series. Total effective resistance
`R_S=200+((400G)/(400+G))`
Now, current in the circuit `I=(V)/(R_S)`
`I=(50)/(200+((400G)/(400+G)))=(50(400+G))/(200(400+G)+400G)`
Pot. difference between A and B `=IR_P=20`
`:. (50(400+G))/(200(400+G)+400G)xx(400G)/(400+G)=20`
or `(50)/(200[400+3G])xx400G=20`
`100G=8000+60G` or `G=200Omega`
When the voltmeter is connected in parallel to the resistance `200Omega`, Net resistance becomes
`R_p^'=(200xx200)/(200+200)=100Omega`
Total resistance of the circuit `=100+400`
`=500Omega`
Current `I^'=(50)/(500)=1/10A`
Reading of voltmeter =Potential difference across `R_p^'`
`=I^'R_p^'=1/10xx100=10V`