A typical galvanometer, which requires a current of 1.50 mA...

A typical galvanometer, which requires a current of $1.50 \mathrm{~mA}$ for full-scale deflection and has a resistance of $75.0 \Omega$, can be used to measure currents of much greater values. A relatively small shunt resistor is wired in parallel with the galvanometer (refer to Fig. $28.24 \mathrm{a}$ ) so that an operator can measure large currents without causing damage to the galvanometer. Most of the current then flows through the shunt resistor. Calculate the value of the shunt resistor that enables the galvanometer to be used to measure a current of $1.00 \mathrm{~A}$ at fullscale deflection. (Hint: Use Kirchhoff's rules.)

Key Concepts

Kirchhoff's Rules

Kirchhoff's rules, including the Current Law (KCL) and Voltage Law (KVL), are fundamental principles in circuit analysis. They allow for the systematic analysis of current and voltage in complex circuits. Specifically, these rules are used to determine how current divides in parallel branches, ensuring accurate calculations when designing circuits that incorporate shunt resistors to achieve full-scale deflection without overloading the measuring device.

Galvanometer

A galvanometer is a sensitive instrument designed to measure small currents, where full-scale deflection corresponds to a specified current level. It operates based on the deflection of a magnetic needle or coil in response to an electric current, serving as an essential tool for detecting and measuring electrical current flow within a circuit.

Shunt Resistor

A shunt resistor is a low-resistance resistor connected in parallel with a measurement device, such as a galvanometer. Its purpose is to divert most of the current around the sensitive instrument, thereby allowing the measurement of larger currents than the device can handle directly and preventing potential damage by ensuring that only a safe amount of current passes through the instrument.

Parallel Circuit Analysis

Parallel circuit analysis involves studying circuits where components are connected side by side, so that they all share the same voltage across them. This concept is crucial for understanding how current divides among multiple parallel paths, such as between a galvanometer and its shunt resistor. By applying the principles of parallel circuits, one can ensure that the device receives only its rated current while the majority flows through the shunt resistor.

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