Basic Electricity

Ohm’s Law Practice Worksheet With Answers

23 questions By Tony R. Kuphaldt

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Question 16 of 23

Shown here is a schematic diagram for a simple battery-powered flashlight:

What could be modified about the circuit or its components to make the flashlight produce more light when turned on?

Reveal answer

Somehow, the power dissipated by the light bulb must be increased. Perhaps the most obvious way to increase power dissipation is to use a battery with a greater voltage output, thus giving greater bulb current and greater power. However, this is not the only option! Think of another way the flashlight’s output may be increased.

Notes:
The “obvious” solution is a direct application of Ohm’s Law. Other solutions may not be so direct, but they will all relate back to Ohm’s Law somehow.
Question 17 of 23

There are two basic Ohm’s Law equations: one relating voltage, current, and resistance; and the other relating voltage, current, and power (the latter equation is sometimes known as Joule’s Law rather than Ohm’s Law):

$$E=IR$$

$$P=IE$$

In electronics textbooks and reference books, you will find twelve different variations of these two equations, one solving for each variable in terms of a unique pair of two other variables. However, you need not memorize all twelve equations if you have the ability to algebraically manipulate the two simple equations shown above.

Demonstrate how algebra is used to derive the ten “other” forms of the two Ohm’s Law / Joule’s Law equations shown here.

Reveal answer

I won’t show you how to do the algebraic manipulations, but I will show you the ten other equations. First, those equations that may be derived strictly from $E = IR$:

$$I= \frac {E}{R}$$

$$R= \frac {E}{I}$$

Next, those equations that may be derived strictly from $P = I E$:

$$I= \frac {P}{E}$$

$$E= \frac {P}{I}$$

Next, those equations that may be derived by using algebraic substitution between the original two equations given in the question:

$$P=I^2R$$

$$P= \frac {E^2}{R}$$

And finally, those equations which may be derived from manipulating the last two power equations:

$$R= \frac {P}{I^2}$$

$$I=\sqrt{\frac{P}{R}}$$

$$E=\sqrt{PR}$$

$$R= \frac {E^2}{P}$$

Notes:
Algebra is an extremely important tool in many technical fields. One nice thing about the study of electronics is that it provides a relatively simple context in which fundamental algebraic principles may be learned (or at least illuminated).

The same may be said for calculus concepts as well: basic principles of derivative and integral (with respect to time) may be easily applied to capacitor and inductor circuits, providing students with an accessible context in which these otherwise abstract concepts may be grasped. But calculus is a topic for later worksheet questions . . .
Question 18 of 23

In this circuit, three resistors receive the same amount of current (4 amps) from a single source. Calculate the amount of voltage “dropped” by each resistor, as well as the amount of power dissipated by each resistor:

Reveal answer

E_{1 Ω} = 4 volts

E_{2 Ω} = 8 volts

E_{3 Ω} = 12 volts

P_{1 Ω} = 16 watts

P_{2 Ω} = 32 watts

P_{3 Ω} = 48 watts

Follow-up question: Compare the direction of current through all components in this circuit with the polarities of their respective voltage drops. What do you notice about the relationship between current direction and voltage polarity for the battery, versus for all the resistors? How does this relate to the identification of these components as either sources or loads?

Notes:
The answers to this question should not create any surprises, especially when students understand electrical resistance in terms of friction: resistors with greater resistance (more friction to electron motion) require greater voltage (push) to get the same amount of current through them. Resistors with greater resistance (friction) will also dissipate more power in the form of heat, given the same amount of current.

Another purpose of this question is to instill in students’ minds the concept of components in a simple series circuit all sharing the same amount of current.

Challenge your students to recognize any mathematical patterns in the respective voltage drops and power dissipations. What can be said, mathematically, about the voltage drop across the 2 Ω resistor versus the 1 Ω resistor, for example?