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Chapter 26: Problem 5

Kirchhoff's Junction Rule states that a) the algebraic sum of the currents at any junction in a circuit must be zero. b) the algebraic sum of the potential changes around any closed loop in a circuit must be zero. c) the current in a circuit with a resistor and a capacitor varies exponentially with time. d) the current at a junction is given by the product of the resistance and the capacitance. e) the time for the current development at a junction is given by the product of the resistance and the capacitance.

Short Answer

Expert verified
a) The algebraic sum of the currents at any junction in a circuit must be zero. b) The algebraic sum of the potential changes around any closed loop in a circuit must be zero. c) The current in a circuit with a resistor and a capacitor varies exponentially with time. d) The current at a junction is given by the product of the resistance and the capacitance. e) The time for the current development at a junction is given by the product of the resistance and the capacitance. Answer: a) and b)

Step by step solution

01

Understanding Kirchhoff's Rules

Kirchhoff stated two rules for electrical circuits: Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). KCL says that the algebraic sum of currents entering a junction is equal to zero, while KVL says that the algebraic sum of the voltage (potential changes) around any closed loop in a circuit is equal to zero. Now, let's analyze the given statements one by one.
02

Analyzing Statement a

Statement a says that "the algebraic sum of the currents at any junction in a circuit must be zero". This statement directly relates to Kirchhoff's current law (KCL), which states that the total current entering a junction must equal the total current leaving the junction. So, statement a is correct.
03

Analyzing Statement b

Statement b says that "the algebraic sum of the potential changes around any closed loop in a circuit must be zero". This statement is equivalent to Kirchhoff's voltage law (KVL), which states that the sum of the voltage gains and drops around a closed loop must be equal to zero. Therefore, statement b is also correct.
04

Analyzing Statement c

Statement c says that "the current in a circuit with a resistor and a capacitor varies exponentially with time." This statement is related to the analysis of an RC (resistor-capacitor) circuit where there is a charging or discharging process happening. This statement, however, is not related to Kirchhoff's Junction Rule. Thus, statement c is not applicable.
05

Analyzing Statement d

Statement d says that "the current at a junction is given by the product of the resistance and the capacitance." This statement is incorrect and not related to Kirchhoff's Junction Rule. The relation between resistance, capacitance, and current is given by Ohm's law, which states that the current flowing through a conductor between two points is directly proportional to the voltage diff across the two points and inversely proportional to the resistance between them.
06

Analyzing Statement e

Statement e says that "the time for the current development at a junction is given by the product of the resistance and the capacitance." While this statement is not related directly to Kirchhoff's Junction Rule, it is a fact about RC circuits. The time constant (τ) of an RC circuit is indeed given by the product of resistance and capacitance (τ = RC), which determines the time it takes for the capacitor to charge or discharge through a resistor. However, since this statement does not relate to Kirchhoff's Junction Rule, it is not applicable. To conclude, only statements a) and b) are related to Kirchhoff's Junction Rule.

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