Question

Find the unknown resistances in this circuit.

   Find the unknown resistances in this circuit.

Physics

Robert Coleman… 5th Edition

Chapter 18, Problem 57

Instant Answer

Solved by Expert Narayan Hari

04/28/2021

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So we have: \[I_3 = I_1 - I_2 = 48mA - 47mA = 1mA\] Show more…

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Find the unknown resistances in this circuit.

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Key Concepts

Ohm's Law

Ohm's Law defines the relationship between voltage, current, and resistance in an electrical circuit, expressing that the voltage across a resistor is equal to the product of the current through it and its resistance (V = IR). This principle is essential for determining unknown quantities in circuits, including resistance.

Kirchhoff's Laws

Kirchhoff's Laws, which include the Voltage Law and the Current Law, are fundamental for analyzing circuits. The Voltage Law states that the sum of the potential differences around any closed loop in a circuit is zero, while the Current Law states that the total current entering a node equals the total current leaving the node. These laws help establish equations that allow the calculation of unknown resistances.

Series and Parallel Resistors

Understanding how resistors connect in series and parallel is key to simplifying complex circuits. In series circuits, resistances add directly, while in parallel circuits, the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. This simplification facilitates the process of finding unknown resistances in a circuit.

Circuit Analysis Techniques

Circuit analysis techniques, such as mesh analysis and nodal analysis, involve setting up and solving systems of equations based on Kirchhoff's Laws and Ohm's Law. These methods provide a systematic approach to determine unknown circuit elements, including resistances, by breaking down complex circuit networks into manageable calculations.

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