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Ch. 26 - DC Circuits
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 26 - DC CircuitsProblem 18
Chapter 25, Problem 18

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]


(II) What is the net resistance of the circuit connected to the battery in Fig. 26–46?

Verified step by step guidance
1
Identify the configuration of resistors in the circuit (series, parallel, or a combination of both) based on the given diagram (Fig. 26–46). This will determine how to calculate the equivalent resistance.
For resistors in series, use the formula: Req=R1+R2+…. Add the resistances directly.
For resistors in parallel, use the formula: 1Req=1R1+1R2+…. Take the reciprocal of the sum of the reciprocals of the resistances.
Simplify the circuit step by step by calculating the equivalent resistance for each group of resistors (series or parallel) until you reduce the entire circuit to a single equivalent resistance.
Once the circuit is reduced to a single equivalent resistance, this value represents the net resistance of the circuit connected to the battery.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Net Resistance

Net resistance in a circuit is the total resistance that current encounters when flowing through the circuit. It can be calculated by combining the individual resistances of components in series and parallel configurations. In series, resistances add up, while in parallel, the reciprocal of the total resistance is the sum of the reciprocals of individual resistances.

Series and Parallel Circuits

In a series circuit, components are connected end-to-end, and the same current flows through each component, resulting in a total resistance that is the sum of all resistances. In contrast, in a parallel circuit, components are connected across the same voltage source, allowing multiple paths for current, which reduces the overall resistance. Understanding these configurations is crucial for calculating net resistance.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed as V = IR. It is fundamental in analyzing electrical circuits, as it helps determine how voltage, current, and resistance interact within the circuit.
Related Practice
Textbook Question

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]


(II) A power supply has a fixed output voltage of 12.0 V, but you need VT = 3.0 V output for an experiment. (a) Using the voltage divider shown in Fig. 26–47, what should R₂ be if R₁ is 16.5 Ω? (b) What will the terminal voltage VT be if you connect a load to the 3.0-V output, assuming the load has a resistance of 7.0Ω?

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Textbook Question

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]


(II) Determine the voltage across each resistor

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Textbook Question

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]


(II) Determine the equivalent resistance of the circuit shown in Fig. 26–44,

Textbook Question

(III) If the 25-Ω resistor in Fig. 26–59 is shorted out (resistance = 0 ), what then would be the current through the 15-Ω resistor?

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Textbook Question

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]


(III) You are designing a wire resistance heater to heat an enclosed container of gas. For the apparatus to function properly, this heater must transfer heat to the gas at a very constant rate. While in operation, the resistance of the heater will always be close to the value R = R₀, but may fluctuate slightly causing its resistance to vary a small amount ∆R ( << R₀ ). To maintain the heater at constant power, you design the circuit shown in Fig. 26–50, which includes two resistors, each of resistance R′. Determine the value for R′ so that the heater power P will remain constant even if its resistance R fluctuates by a small amount. [Hint: If ∆R << R₀ , then ΔP≈ΔRdPdR∣R=R0\(\Delta\) P\(\approx\) \(\Delta\) R\(\left\). \(\frac{dP}{dR}\]\right\)|_{R=R_{0}}]

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Textbook Question

[In these Problems neglect the internal resistance of a battery unless the Problem refers to it.]


(II) Determine the current through each resistor.

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