Question

A $10-\Omega, 15-\Omega,$ and $5-\Omega$ resistor are connected in a series circuit with a $90-\mathrm{V}$ battery. What is the equivalent resistance of the circuit? What is the current in the circuit?

   A $10-\Omega, 15-\Omega,$ and $5-\Omega$ resistor are connected in a series circuit with a $90-\mathrm{V}$ battery. What is the equivalent resistance of the circuit? What is the current in the circuit?

Physics Principle and Problems

Physics Principle and Problems

Paul W. Zitzewitz,… 1st Edition

Chapter 23, Problem 2

Instant Answer

Solved by Expert Adithya Ramanujam

05/24/2020

Step 1

Since the resistors are connected in series, we can simply add up their resistances. The formula for the equivalent resistance (R_eq) of resistors in series is: \[R_{eq} = R_1 + R_2 + R_3 + ... + R_n\] In our case, we have three resistors with resistances of 10 Show more…

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A $10-\Omega, 15-\Omega,$ and $5-\Omega$ resistor are connected in a series circuit with a $90-\mathrm{V}$ battery. What is the equivalent resistance of the circuit? What is the current in the circuit?

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Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electrical engineering and physics that defines the relationship between voltage, current, and resistance in a circuit. It is expressed by the formula V = IR, where V is the voltage across the circuit, I is the current flowing through it, and R is the resistance. This law allows for the calculation of any one of these values when the other two are known.

Equivalent Resistance

Equivalent resistance is a single resistance that can replace a network of resistors without changing the overall current in the circuit. In series circuits, the equivalent resistance is simply the sum of the separate resistors. This concept simplifies the analysis of circuits by reducing complex resistor networks to a single resistance value.

Series Circuit

In a series circuit, electrical components are connected one after the other so that the same current flows through each component. This implies that the overall resistance of the circuit is the sum of the individual resistances, and any power source’s voltage is divided among the components according to their resistances.

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