Question

A voltmeter of resistance 400 ohms is used to measure the potential difference across the 100 ohms resistor in the circuit shown in the figure (a) What will be the reading of the voltmeter? (b) What was the potential difference across 100 ohms before the voltmeter was connected?​

Answer 1

Given :

The potential difference applied in the circuit = 84 V

Resistance of the voltmeter = 400 ohm

Resistances connected in the given circuit = 100 ohm and 200 ohm

The voltmeter is connected across the resistor to measure the potential differnece is 100 ohm .

To Find :

(a) The reading of the voltmeter = ?

(b)The potential difference across 100 ohms before the voltmeter was connected =?​

Solution :

The current through the circuit using Ohm's Law  will be given as :

$I = \frac{V}{R}$

Here , V is applied potential difference to the circuit and R is the equivalent resistance .

The equivalent resistance R will be given as:

100 ohm and 400 ohm are connected in parallel and this combination is in series with the 200 ohm .

So, $R = \frac{100 \times 400 }{100 + 400}+ 200$

         =$\frac{40000}{500} + 200$

         = 80 + 200

         = 280 ohm

So, $I = \frac{84}{280}$ A

Now reading of the voltmeter will be equal to potential difference across it or the potential difference across the combination of 100 ohm resistor and voltmeter .

So, Reading = $I\times r$     ( here r is eqv. resistance of 100 ohm and voltmeter )

                    =$\frac{84}{280}\times 80$

                    = 24 V

Now for the 2nd part i.e. when voltmeter is not connected :

In this case the two resistors 100 ohm and 200 ohm will be series .

So , the equivalent resistance is :

R' =200 +100

   = 300 ohm

So, the current in he circuit using Ohm's law will be :

$I' = \frac{V}{R'}$

   =$\frac{84}{300}$ A

And the potential difference across the 100 ohm resistor will b :

$V_{100} = I'\times 100$

       =$\frac{84}{300}\times 100$

       = 28 V

Hence , the reading of the voltmeter is 24 V  and the potential difference  across 100  ohm resistor when  voltmeter was not connected is 28 V .

                   

Answer 2

Answer:

A) 24 v

B) 28 V