Question

An ammeter and a voltmeter are connected in series to a battery with an emf $e=6.0V$. When a certain resistance is connected in parallel with the voltmeter , the reading of the voltmeter decreases $2.0$ times , whereas the reading of the ammeter increases the same number of times. Find the voltmeter reading after the connection of the resistance.
A. $2V$
B. $4V$
C. $8V$
D. $18V$

Answer 1

Hint: We studied current electricity, in this type of question we use the basic concept of an ammeter and voltmeter. Both the ammeter and the voltmeter are connected in the current carrying circuit for measurement of the current and voltage respectively.

Complete step by step answer:
When the current follows through there is a potential difference between the two points in the electrical circuit, this potential difference is measured by a voltmeter and then an ammeter is used to measure the electric current. For measuring the current and the voltage, these devices are connected series and parallel with the measuring device respectively. A standard voltmeter and ammeter alter the circuit's measurements due to withdrawing of some extra current and by decreasing the current flow respectively.

In the given question, An ammeter and a voltmeter are connected in series to a battery with an emf $e=6.0V$. Initially, only the resistance of ammeter is presents i.e. $R$ and the voltage drop occurs only in voltmeter i.e. $V$. Hence,

$V=6-iR$, where $i$ is current in circuit.
$i={\displaystyle \frac{6-V}{R}}$

When a certain resistance is connected in parallel with the voltmeter , the reading of the voltmeter decreases $2.0$ times , whereas the reading of the ammeter increases the same number of times. So,

                                  

$$\begin{gathered} V_f=V/2,i_f=2i \\ {V}_f=6-i_{f}R \\ V/2=6-2iR \end{gathered}$$

After putting the value of current,

$$\begin{gathered} {\displaystyle \frac{V}{2}}=6-2R({\displaystyle \frac{6-V}{R}}) \\ V=2(2V-6) \\ V=4V-12 \\ V=4 \end{gathered}$$

The voltmeter reading after the connection of the resistance 4 volt.

So, the correct answer is “Option B”.

Note:
Ammeter has low resistance and the voltmeter has high internal resistance. For the ideal ammeter, resistance is zero. If the resistance of the ammeter is high it will alter the measurements of the flowing current that is why it should be low.