Question

To convert $800mV$ range milli-voltmeter of resistance $40\Omega $ into a milli ammeter of $100mA$range, resistance to be connected in shunt is
$\begin{align}
  & a)10\Omega \\
 & b)5\Omega \\
 & c)2.5\Omega \\
 & d)1\Omega \\
\end{align}$

Answer 1

Hint: Resistance that must be connected as shunt to convert a voltmeter to millimetre is usually connected in parallel. So, we have to connect a resistance unknown parallel to $40\Omega $. Now, the current produced by the voltmeter is equal to the given ammeter reading. Find the resistance easily.
Formula used:
$V=IR$

Complete answer:
Let us consider the shunt resistance as r. We know, the resistance connected must be parallel to the voltmeter resistance to convert it into an ammeter. Therefore,
${{R}_{net}}=\dfrac{40\times R}{40+R}$
Therefore, the current in voltmeter is equal to ammeter.
$\begin{align}
  & \Rightarrow \dfrac{800}{\dfrac{40R}{40+R}}=100 \\
 & \Rightarrow 320+8R=40R \\
 & \Rightarrow 32R=320 \\
 & \Rightarrow R=10\Omega \\
 & \\
\end{align}$

So, the correct answer is “Option A”.

Additional Information:
The sum of voltages consumed by each individual resistance is equal to the source voltage in a series circuit. Whereas in parallel circuits, the current through each resistance is equal. In series combination, the voltage across the resistors connected is different. In parallel combinations, the current through the resistors present is different. The equivalent resistance in a series combination is greater than the given resistances. Whereas, in parallel combinations, the equivalent resistance is smaller than the individual resistances.



Note:
When we convert an ammeter to voltmeter, the resistance must be connected in series, whereas while converting form voltmeter to ammeter, the resistor must be connected in parallel. An ammeter only works when it is connected in parallel to the circuit, a voltmeter works only when it is connected in series to the circuit.