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Ohm's Law is one of the fundamental principles used in the field of electronics and electrical engineering. It states that the voltage across a conductor is directly proportional to the current flowing through it, given that the temperature and the material's properties remain constant. The law is formally expressed as:

• \[ V = I \times R \]

Here, \( V \) is the voltage in volts, \( I \) is the current in amperes, and \( R \) is the resistance in ohms. In the context of the galvanometer problem, Ohm's Law was applied to calculate the voltage drop across the galvanometer. Given the resistance \( (R_g = 20.0 \; \Omega) \) and the current \( (I_g = 6.20 \; \text{mA}) \), we calculated the potential difference \( (V_g) \) as follows:

• \[ V_g = I_g \times R_g = 6.20 \times 10^{-3} \times 20.0 = 0.124 \; \text{V} \]

This voltage value is crucial, as it is also the voltage across the shunt resistor when full scale deflection is reached. Understanding Ohm's Law allows you to relate current, voltage, and resistance, which are essential components when analyzing circuits.

A shunt resistor is a very low resistance component used in parallel with a device (like a galvanometer) to allow a large portion of the current to bypass the device. It is typically used to extend the range of measuring instruments, such as converting a galvanometer into an ammeter allowing it to measure high current levels. When a shunt resistor \((R_s = 24.8 \; \text{m} \Omega)\) is connected in parallel with the galvanometer, it shares the current:

• Most of the current flows through the shunt due to its much lower resistance compared to the galvanometer.
• This ensures the galvanometer is protected from high current levels that could damage it.

With the potential difference across both the galvanometer and shunt remaining the same, Ohm's Law is used to find the current through the shunt \((I_s)\). For example:

• \[ I_s = \frac{V}{R_s} = \frac{0.124}{24.8 \times 10^{-3}} = 5.0 \; \text{A} \]

This large current passes through the shunt while only a very small fraction passes through the galvanometer. The design allows the galvanometer to safely measure higher currents.

The primary goal in the conversion of a galvanometer to an ammeter is to enable it to measure larger currents than it could on its own. The maximum current measurable by the ammeter \((I_{max})\) is the sum of the current through the galvanometer and the current through the shunt resistor.

• The initial current through the galvanometer \(I_g\) is only 6.20 mA.
• The added shunt allows most of the current, in this case \(I_s = 5.0 \; \text{A}\), to bypass the galvanometer.

To find the total maximum current, you simply sum these two quantities:

• \[ I_{max} = I_g + I_s = 6.20 \times 10^{-3} + 5.0 = 5.0062 \; \text{A} \]

Hence, the ammeter can safely read currents up to approximately \(5.0062 \; \text{A}\). This conversion is essential for practical applications where current measurements exceed the device's original range.