The 5.00 Vbattery in Fig. E26.26 is removed from the circuit...

The $5.00 \mathrm{Vbattery}$ in Fig. E26.26 is removed from the circuit and replaced by a $15.00 \mathrm{~V}$ battery, with its negative terminal next to point $b$. The rest of the circuit is as shown in the figure. Find (a) the current in each branch and (b) the potential difference $V_{a b}$ of point $a$ relative to point $b$.

Key Concepts

Kirchhoff's Voltage Law

This principle states that the sum of all the voltage gains and drops around any closed circuit loop must equal zero. In circuit analysis, it is used to write equations relating the electromotive forces (like batteries) and voltage drops (across resistors) in various loops. This law is essential for solving for unknown quantities such as branch currents and potential differences between points in the circuit.

Kirchhoff's Current Law

Kirchhoff's Current Law asserts that the total current entering any junction in a circuit must equal the total current leaving that junction. This principle is fundamental when analyzing circuits with multiple branches, as it allows us to establish relationships between the various branch currents. It ensures the conservation of electric charge at the nodes of a circuit.

Ohm's Law

Ohm's Law is a basic relation in electronics that connects the voltage (V), current (I), and resistance (R) in a resistor through the formula V = IR. This law is indispensable in circuit analysis as it allows for the computation of the voltage drop across a resistor when the current flowing through it and its resistance are known, and vice versa.

Circuit Loop Analysis

Circuit loop analysis involves breaking a circuit down into its individual loops and applying Kirchhoff's Voltage Law to each loop. This method is particularly useful when dealing with circuits that have multiple loops and branches since it provides a systematic approach to setting up simultaneous equations to solve for unknown currents and voltages.

Potential Difference and Reference Points

Potential difference, often referred to as voltage, is the difference in electric potential between two points in a circuit. Setting a reference point (or ground) is crucial in circuit analysis because it provides a common point from which all other potentials are measured. Understanding the concept of potential difference is key to determining the voltage drops across components and the relative voltage between any two points in a circuit.

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