Help for Wizard Difficulty Level
You can think of this difficulty level as involving six problems. Each row is a problem. And each row is independent of any other row. That is, for Row B, all you need to know is Row B information in order to determine the blanks of Row B. There are four ideas that you will use in determining the four blanks in each row. Here they are:
Equivalent or Total Resistance
We refer to a circuit like this as being a series circuit because there are two resistors that are arranged in series. When there is a series arrangement of two resistors, all the charge that passes through one resistor will also pass through the second resistor. For a series circuit, the total resistance is the sum of the individual resistance values. This sum is known as the equivalent resistance or total resistance. So columns 2, 3 and 4 of the table are related. If you know two of them, you can calculate the third one.
Comparing Currents at Different Locations
The fifth and sixth columns of the table have the headings - Current at A and Current at C. Here the letters A and C refer to two different locations in the series circuit. In a series circuit, the current is everywhere the same. It doesn't matter if one location is closer to the + terminal and another further from the + terminal of the battery. The fact is that charge is marching through the wires of the circuit together and the rate at which it marches is independent of the location. So if you know the value in any of these two columns for any row, then you also know the values for the other column; they are the same.
Voltage-Current-Resistance
One of the most pervasive formulas in electricity is ∆V = I•R. The difference in electric potential between the + and - terminals of the battery is equal to the resistance multiplied by the current. The difference in electric potential is simply the battery voltage and is listed in the first column. Using this equation, the first column (Battery Voltage), the fourth column (Equivalent Resistance, Req), and any one of the fifth and sixth columns (Current) can be related. Knowing two of these three columns, you can calculate the third column.
Electric Potential at Location B
For a 12-volt battery, the difference in electric potential between the two terminals is 12 volts. We'd say that the positive terminal (the one closest to location A) is at 12 volts potential and the negative terminal (the one closest to location C) is at 0 volts. The same reasoning applies to a 6-volt, an 18-volt, and a 24-volt battery. In the last column, you have to determine the electric potential at location B. Think of this location as being located one resistor past location A and one resistor before location C.
Electric charge will lose potential (or volts) as it passes from location A to location B. The amount of loss is simply I•R where I is the current in the circuit and R is the resistance of resistor 1 (located between location A and B). When you use the ∆V = I•R equation, you are calculating the difference in electric potential or voltage drop occuring as charge passes between these two locations. Knowing this rule allows one to determine the electric potential at location B for Rows A through D. In Row E and F, this value is given, you can subtract it from the battery voltage to determine the voltage drop from Location A to B. Once done, you can use this voltage drop to determine the resistance of Resistor 1 (Row E) or the current in the circuit (Row F).