Ch. 25 - Electric Current and Resistance

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 25 - Electric Current and Resistance

Problem 86a

Chapter 24, Problem 86a

Lightbulb A is rated at 120 V and 40 W for household applications. Lightbulb B is rated at 12 V and 40 W for automotive applications. What is the current through each bulb?

Verified step by step guidance

Step 1: Recall the formula for power in an electrical circuit:

P = V I

, where

P

is power,

V

is voltage, and

I

is current. Rearrange this formula to solve for current:

I = P / V

Step 2: For Lightbulb A, substitute the given values into the formula. The power

P

is 40 W, and the voltage

V

is 120 V. The current

I

can be calculated as

I = 40/120

(in amperes).

Step 3: For Lightbulb B, substitute the given values into the same formula. The power

P

is 40 W, and the voltage

V

is 12 V. The current

I

can be calculated as

I = 40/12

(in amperes).

Step 4: Ensure that the units are consistent throughout the calculation. Power is in watts (W), voltage is in volts (V), and current will be in amperes (A).

Step 5: After substituting the values and performing the division, you will have the current for each bulb. Remember to double-check your calculations for accuracy.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

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. It is mathematically expressed as I = V/R. This principle is fundamental for calculating current in electrical circuits, especially when voltage and resistance are known.

Power in Electrical Circuits

The power (P) consumed by an electrical device is defined as the product of the voltage (V) across it and the current (I) flowing through it, expressed as P = V × I. This relationship allows us to determine the current if the power rating and voltage are known, which is essential for solving the problem regarding the lightbulbs.

Series and Parallel Circuits

Understanding whether components are connected in series or parallel is crucial for analyzing electrical circuits. In a series circuit, the same current flows through all components, while in a parallel circuit, the voltage across each component is the same. This distinction affects how we calculate current and power for devices like lightbulbs, which can be connected in different configurations.

Recommended video:

Guided course

09:51

Combining Capacitors in Series & Parallel

Related Practice

Textbook Question

The level of liquid helium (temperature ≈ 4K) in its storage tank can be monitored using a vertically aligned niobium–titanium (NbTi) wire, whose length ℓ spans the height of the tank. In this level-sensing setup, an electronic circuit maintains a constant electrical current I at all times in the NbTi wire and a voltmeter monitors the voltage V across this wire. The NbTi wire is superconducting ( R = 0) if below its transition temperature of 10 K, so the portion of the wire immersed in the liquid helium is in the superconducting state, while the portion above the liquid (in helium vapor with temperature above 10 K) is in the normal state. Define ƒ = x/ℓ to be the fraction of the tank filled with liquid helium (Fig. 25–40) and V₀ to be the value of the voltage V when the tank is empty (ƒ = 0) . Determine the relation between f and V (in terms of V₀).

views

Textbook Question

A 100-W, 120-V incandescent lightbulb has a resistance of 12 Ω when cold (20°C) and 150 Ω when on (hot). Calculate its power consumption (a) at the instant it is turned on, and (b) after a few moments when it is hot.

views

Textbook Question

A 2800-W oven is connected to a 240-V source. How long will it take to bring 150 mL of 15°C water to 100°C assuming 65% efficiency?

views

Textbook Question

Lightbulb A is rated at 120 V and 40 W for household applications. Lightbulb B is rated at 12 V and 40 W for automotive applications. What is the resistance of each bulb?

views

Textbook Question

Suppose a current is given by the equation I = 1.40 sin 210t, where I is in amperes and t in seconds. What is the rms value of the current?

views

Textbook Question

Copper wire of diameter 0.259 cm is used to connect a set of appliances at 120 V, which draw 1250 W of power total. What power is wasted in 25.0 m of this wire?

views