Otis Singleton
Solving electricity problems in physics involves understanding the relationship between power, voltage, current, and resistance. Power is the rate of energy use or conversion, and electric power is calculated by multiplying current and voltage. In a circuit, the current remains the same for resistors in series, while the voltage drop stays the same for resistors in parallel. To solve for current or voltage, one can use Kirchhoff's Laws or apply Ohm's Law, which relates power, voltage, and current to resistance. Induction problems, which are unique to electricity and magnetism, can be understood through the EMF equation, where EMF is related to the change in magnetic flux. By recognizing the problem type, one can use the appropriate equations and principles to solve for unknown values, such as power, resistance, current, or voltage.
| Characteristics | Values |
|---|---|
| Definition problems | Definition of terms such as current, voltage, resistance, power, energy, etc. |
| Dynamics (force) problems | Understanding the relationship between voltage, current, and resistance in a circuit |
| Conservation of Energy problems | Applying the principle of energy conservation in electrical circuits |
| Circuit problems | Identifying resistors or capacitors in a circuit and calculating current or charge |
| Induction problems | Understanding EMF and its relationship with magnetic flux and induced current |
| Calculating power | Multiplying current and voltage (P=IV) or using other formulas like P=QV/t or P=V^2/R |
| Calculating energy | Understanding the relationship between power, energy, and time (Energy=Power*Time) |
| Cost of electricity | Multiplying power, time, and cost per unit of power (Cost=PowerTimeRate) |
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What You'll Learn
Circuit problems
The first step in solving circuit problems is to calculate the equivalent resistance of the circuit. First, combine all the series resistors and then calculate the parallel ones. Resistors in series have the same current, while the voltage drop is the same across resistors in parallel.
Next, apply the loop rule to all the loops in the circuit to find the relationship between voltage drops and the EMF of the battery. The voltage drops can be found using Ohm's law. Verify your calculations by adding the voltage drops. In a series circuit, they should equal the voltage increase of the power supply.
Finally, remember the key ideas of Conservation of Charge and Conservation of Energy. Conservation of Charge tells us that electrons are not used up in resistors; they only lose some of their electric potential energy.
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Definition problems
Quantifying electric fields in definition problems involves restating the charge and location information in a slightly different way. For instance, if you are given information about the material out of which a resistor or capacitor is made, you have a definition problem rather than a circuit problem.
In some cases, definition problems can be more complicated because the desired quantities are vectors. This means that you will need to do additional math to divide vectors into components. For example, if you are given the angle shown in a figure, the y-component of electric force is opposite the angle, and the x-component is adjacent. The key to solving this type of problem is understanding that both parts are definition problems, and the mathematical effort lies in finding the vector sum.
It is important to note that definition problems do not always require pictures. However, in cases where vector addition is required, it is helpful to include visuals.
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Dynamics (force) problems
When approaching force problems, it is helpful to create a free-body diagram. This diagram will allow you to visualize what is happening and directly map the picture into the equation. First, identify the object(s) or system(s) that will be the focus of the diagram. In some cases, you may need to consider multiple objects as separate systems and draw individual free-body diagrams for each. Newton's Third Law can be used to relate the forces acting on two objects.
Once you have identified the system, consider all the forces acting on it. Discard any forces that are negligible or too small to matter. Only the forces acting on the object should be included in the diagram, as you are trying to understand what causes its motion. Acceleration, if needed, should be sketched separately from the sketch of forces. Remember that acceleration is the result, not the cause.
Since Newton's Second Law is a vector equation, you will need to divide all forces into their x- and y-components. It is often easiest to choose one axis to be along the direction of acceleration, making one component of acceleration zero and reducing the number of linked equations. All force problems start with the relation ∑F=ma. If you need additional information, it will typically become apparent as you work through the problem.
After you have filled in the equations, you are left with algebra. Generally, it is easiest to solve the equation where acceleration (a) is zero first, as you may need those values in other expressions. Once you have solved the equations, review your answer critically. Does it make sense intuitively? Can you explain what is happening in words? This reflective step is important to solidify your understanding of the problem and identify areas for improvement.
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Induction problems
To solve such problems, you need to consider the strength of the magnetic field, the size of the loop, and the orientation of the loop with the magnetic field. The magnetic flux through a loop is represented by the Greek letter Phi (Φ). It is important to remember that an induced current will always work to oppose the change in flux through the loop. This means that its magnetic field will oppose the change in the original magnetic field.
When solving induction problems, you will often need to use the two-step right-hand rule. First, point your thumb in the direction of either the current (I) or the magnetic field (B), whichever is straight. Second, the direction in which your fingers curl will give you the direction of the remaining vector (I or B).
Additionally, when solving induction problems, you may need to manipulate equations involving Δ__/Δt, which represents the change in magnetic flux with respect to time. The approach to solving these equations remains the same, regardless of changes in the size or orientation of the loop. You can usually leave variables such as the size of the loop (A) and the angle between B and A (θ) inside the Δ__/Δt operator, while keeping other variables constant.
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Conservation of Energy problems
The law of conservation of energy states that the total energy of an isolated system remains constant over time. In other words, energy can neither be created nor destroyed, only transformed from one form to another. This principle was first outlined by Karl Friedrich Mohr in 1837, and later by Hermann von Helmholtz in 1847, building on the work of William Robert Grove in 1844.
When solving conservation of energy problems in physics, it is important to identify the different forms of energy involved and how they are transformed. For example, in the case of a stick of dynamite exploding, chemical energy is converted to kinetic energy, potential energy, heat, and sound. To calculate the total energy of the system before and after the explosion, one must sum up all these forms of energy and ensure they balance out.
In electricity and magnetism problems, the conservation of energy is a key principle. For example, in a circuit with resistors and capacitors, the conservation of energy tells us that electrons are not used up in resistors but instead give up some of their electric potential energy. This is known as the conservation of charge.
- A hairdryer with a charge of 350 C moves through a potential difference of 20 V for 4 minutes. How much power is transformed? (Answer: 29.2 W)
- Calculate the resistance of an electric blanket that draws 9 A to transform 50 W of energy. (Answer: 0.6173 ohms)
- How many joules of energy are necessary to run a television for 30 minutes if it is hooked up to a 120-V line and has a resistance of 6 ohms? (Answer: 4.32 x 10^6 joules)
- A generator produces 140 kW of power and delivers electricity at 6000 V. How much current is being received? If the voltage is increased to 10,000 V, how much less current will be received? (Answer: 23.3 A initially, 9.3 A less at higher voltage)
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Frequently asked questions
Use the formula P=QV/t. For example, if a hairdryer with a 350 C charge moves through a potential difference of 20 V for 4 minutes, the power transformed is 29.2 W.
Use the formula P=I^2 R. For example, if an electric blanket draws 9 A to transform 50 W of energy, the resistance is .6173 ohms.
First, calculate the power in kilowatts, then multiply this by the number of hours used and the cost per kilowatt-hour. For example, a refrigerator that requires 3.5 kW and is used for 6 months at a rate of $0.05 per kWh will cost $756.
Use the formula EMF = IR. For example, if a microwave transforms 50 W of energy when linked to a 20-V source, the induced current is 2.5 A.
