Question

The range of voltmeter of resistance $300\Omega $ is 5V. The resistance to be connected to convert it into an ammeter of range 5A is:
A. $1\Omega $ in series
B. $1\Omega $ in parallel
C. $0.1\Omega $ in series
D. $0.1\Omega $ in parallel

Answer 1

Hint: Voltmeters are connected parallel to the circuit with very high resistances so that they don’t draw a lot of current, but ammeters are connected in series and for that the resistance of the voltmeter must be reduced. One easy way to do it is add a small resistance in parallel to the voltmeter and calculate the amount of current at the maximum and minimum reading of the voltmeter to get the value of current flowing through the circuit.

Formula used:
Ohm’s Law
$V=IR$
Equivalent resistance of two resistors connected in parallel
$\dfrac{1}{R}=\dfrac{1}{{{R}_{1}}}+\dfrac{1}{{{R}_{2}}}$

Complete answer:
As we know that voltmeters are connected in parallel to the circuit, but ammeters need to be connected in series, we will reduce the resistance of the voltmeter by connecting a small resistance in parallel to the voltmeter. First, we will make a circuit diagram of the voltmeter and the resistance connected in parallel to visualize the situation.

The setup shown on whole will act as an ammeter. We will find the resistance that the complete setup needs to have so that the current flowing through it is 5A when the voltage applied across it is 5V. A simple use of the Ohm’s law will show that the resistance will need to be ${{R}_{total}}=\dfrac{V}{I}=\dfrac{5}{5}=1\Omega $. This is the resistance of the combination of both the resistances. So, we get the equation
$\begin{align}
  & \dfrac{1}{{{R}_{total}}}=\dfrac{1}{R}+\dfrac{1}{300}\Rightarrow \dfrac{1}{R}=\dfrac{1}{1}-\dfrac{1}{300}\approx 1 \\
 & \therefore R=1\Omega \\
\end{align}$

So, the correct answer is “Option B”.

Note:
Knowledge of how ammeter and voltmeter are connected in a circuit and what their resistances must be in order to least affect other parts of the circuit is necessary here. The actual resistance of the setup when we chose the given resistance will actually be a little bit less than the required resistance, but the change is so low it can be ignored without any effect.