Question

A galvanometer of resistance \(200 \Omega\) gives full scale deflection with 15 milli-ampere current. In order to convert it into a \(15 \mathrm{~V}\) range voltmeter. What is the value of resistance connected in series ? (A) \(1000 \Omega\) (B) \(800 \Omega\) (C) \(2500 \Omega\) (D) \(1500 \Omega\)

Short answer

The value of the series resistance needed to convert the galvanometer into a 15 V range voltmeter is \(800 \Omega\). The correct answer is (B) \(800 \Omega\).

Step-by-step solution

Recall Ohm's Law

Ohm's Law states that voltage (V) is equal to the product of current (I) and resistance (R): V = IR. We will use this equation to determine the value of the series resistance needed to convert the galvanometer into a voltmeter.

Calculate the voltage across the galvanometer

We are given that the full-scale deflection current of the galvanometer is 15 mA (or 0.015 A). To find the voltage across the galvanometer, we'll use Ohm's Law (V = IR) with the given resistance of 200 Ω: V_galvanometer = I_galvanometer × R_galvanometer V_galvanometer = (0.015 A) × (200 Ω) V_galvanometer = 3 V

Determine the voltage across the series resistance

Since we want to convert the galvanometer into a 15 V range voltmeter, the total voltage across both the galvanometer and the series resistance (R_series) must be 15 V. To find the voltage across the series resistance, we'll subtract the voltage across the galvanometer from the total voltage: V_series_resistance = V_total - V_galvanometer V_series_resistance = 15 V - 3 V V_series_resistance = 12 V

Calculate the value of the series resistance

Now we have the voltage across the series resistance and we know that the current through it is the same as the current through the galvanometer (15 mA or 0.015 A). Using Ohm's Law (V = IR), we can solve for the value of the series resistance: R_series = V_series_resistance ÷ I_galvanometer R_series = 12 V ÷ 0.015 A R_series = 800 Ω The value of the series resistance needed to convert the galvanometer into a 15 V range voltmeter is 800 Ω. The correct answer is (B) 800 Ω.

Key concepts

Understanding Ohm's Law

Ohm's Law is a fundamental principle used to relate the voltage, current, and resistance in electrical circuits. It is expressed as:

• Voltage (V) = Current (I) × Resistance (R)

This equation forms the foundation for analyzing circuits.
To solve for any one of these variables, you need to know the other two.
For example, if you know the current and resistance, you can use Ohm's Law to find the voltage by multiplying the current by the resistance.
This concept is crucial when dealing with a galvanometer, which is a device that measures small electric currents.

Exploring Series Resistance

Series resistance occurs when two or more resistors are connected end-to-end, creating a single path for current.
In such a connection, the total resistance is simply the sum of all individual resistances.
This characteristic is important in modifying a device's measurement range.

• Total resistance in series, \( R_{total} = R_1 + R_2 + ... + R_n \)

In the galvanometer-to-voltmeter conversion process, a series resistance is added to expand the voltage measurement range.
The additional resistance limits the current, ensuring the galvanometer operates within its safe measurement range.
This alteration prevents damage and allows for precise voltage measurements over a larger range.

Voltmeter Conversion Procedure

Converting a galvanometer into a voltmeter involves adding a series resistance to extend its voltage measuring capabilities. Here's how it works:

• Calculate the voltage across the galvanometer using Ohm's Law.
• Subtract this value from the desired total voltage measurement range.
• Use Ohm's Law again to determine the necessary series resistance.

In the context of converting the galvanometer into a 15 V range voltmeter, initially find the voltage across the galvanometer. This is done using its internal resistance and full-scale deflection current.
Next, you determine the voltage across the series resistance needed to achieve the full 15 V range.
Knowing this voltage and the current, you can calculate the series resistance, ensuring accurate readings without surpassing the galvanometer's current limit.

Full Scale Deflection Explained

Full-scale deflection refers to the maximum current that a galvanometer can measure before the needle reaches its maximum position.
This is a critical parameter, as it defines the upper limit of current the device can handle safely.

• In our example, this value is 15 mA.

By knowing the full-scale deflection, it helps choose the right series resistance for voltmeter conversion.
This allows the galvanometer to measure a broader range of voltages while ensuring the current never exceeds the galvanometer's safe operating conditions.
The right series resistance maintains device integrity and measurement accuracy, making full-scale deflection a vital consideration in circuit adjustment.