Question

An ammeter of range $5\mathrm{A}$ is to be converted into an voltmer of range $10\mathrm{V}$. If the resistance of ammeter be $0.1$, then what resistance should be connected in series with it ? (A) $4.9\mathrm{\Omega }$ (B) $2.1\mathrm{\Omega }$ (C) $1.1\mathrm{\Omega }$ (D) $1.9\mathrm{\Omega }$

Short answer

The resistance that should be connected in series with the ammeter to convert it into a voltmeter of range 10V is $1.9\mathrm{\Omega }$. The correct answer is (D).

Step-by-step solution

Find the internal resistance of the ammeter

It is given that the resistance of the ammeter is 0.1 Ω. Let's denote this internal resistance as R_a. So, R_a = 0.1 Ω

Find the current flowing through the ammeter

The maximum current that the ammeter can measure is 5 A. It is given in the problem and we will denote it as I. So, I = 5 A

Calculate the current through the voltmeter

We need to convert the ammeter into a voltmeter with a range of 10 V. Let's denote this voltage range as V. So, V = 10 V Now, use the Ohm's Law to find the current through the voltmeter (I_v). I_v = V / (R_a + R)

Calculate the resistance required in series

In this step, we will calculate the resistance (R) that should be connected in series with the ammeter to convert it into a voltmeter. From Step 3, we have the relation: I_v = V / (R_a + R) We know that I_v = I, V = 10 V, and R_a = 0.1 Ω. Substitute these values in the equation and solve for R. I = 10 / (0.1 + R) 5 = 10 / (0.1 + R) Rearrange the equation and solve for R: R = (10 / 5) - 0.1 = 2 - 0.1 = 1.9 Ω So, the resistance that should be connected in series with the ammeter is 1.9 Ω. The correct answer is (D).

Key concepts

Ammeter

An ammeter is a device used to measure electric current in a circuit. It is designed to measure current in units of amperes (A). To safely and accurately measure current, an ammeter must have a very low internal resistance. This is because it is connected in series with the circuit, and a low resistance ensures it does not significantly alter the current it is measuring.
Ammeters are specifically designed to handle a maximum current without being damaged, which is its range limit. For instance, if an ammeter has a range of 5 A, it means it can accurately measure currents up to 5 amperes without the risk of damage. Understanding how ammeters work is crucial when modifying them to perform other functions, like measuring voltage.

Voltmeter range conversion

To convert an ammeter into a voltmeter, we modify its ability to measure voltage instead of current. This involves adding additional resistance in series with the ammeter. This ensures that the device can measure voltage across a circuit rather than just passing current through it.

When converting a 5 A ammeter with 0.1 Ω resistance into a voltmeter with a 10 V range, we need to calculate the appropriate series resistance. This process ensures that the converted device measures the correct voltage across a specified range without damage or incorrect readings.

• The core formula used here is Ohm's Law, which states that $V=IR$.
• By rearranging Ohm's Law to $I=\frac{V}{R}$, we can solve for the required series resistance $R$.

This calculation safeguards the device's accuracy in measuring voltage, allowing it to function effectively as a voltmeter.

Internal resistance

Internal resistance is the inherent resistance found within any electrical device, including ammeters. This internal resistance affects how the device functions within a circuit, influencing both current measurement accuracy and energy loss as heat.

For an ammeter, having very low internal resistance is ideal because it reduces the impact on the circuit and allows more precise current measurements. However, this characteristic is crucial when converting an ammeter to a voltmeter. The known internal resistance of the ammeter (0.1 Ω in our case) must be factored in when calculating the additional resistance required in series.
Understanding internal resistance is important because it helps in predicting and controlling how an ammeter or converted voltmeter will behave in various circuit conditions, ensuring that measurements remain accurate and the device stays safe under operation.

Series resistance calculation

Series resistance calculation is key when converting an ammeter to a voltmeter. This calculation ensures that the modified device can safely operate within its new parameters.
To determine the necessary series resistance, we can follow these steps:

• Identify the maximum current the ammeter can handle, which is 5 A in this case.
• Determine the desired voltage range, which here is 10 V.
• Use Ohm's Law, rearranged as $R=\frac{V}{I}-R_a$, where $R_a$ is the internal resistance.
• Substitute the known values: $R=\frac{10}{5}-0.1=2-0.1=1.9\Omega$.

This calculated series resistance of 1.9 Ω allows the converted voltmeter to accurately measure up to 10 V without being overloaded, effectively expanding its functional range from current to voltage measurement.