Help for Master Difficulty Level
You can think of this difficulty level as involving five 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 three ideas that you will use in determining the blanks in each row. Here they are:
Only Two Potentials or Voltages
The battery maintains a difference in electric potential or voltage between the two terminals of the battery. Any wire attached to the + terminal has the electric potential or voltage of the + terminal. Similarly, any wire attached to the - terminal has the electric potential or voltage of the - terminal. Locations A, B and C are each located on a wire attached to the + terminal. Each of these locations has a voltage equal to the battery voltage. And Location D and all other unmarked locations on the lower side of the diagram (below the resistors) has a voltage of 0 Volts - equal to the voltage of the - terminal. Those are the only two voltages of wires in each of the circuits (or rows). And so the electric potential difference across each of the resistors is equal to the battery voltage. If the battery voltage is 12 Volts, there there is a 12-volt ∆V across each of the resistors of the parallel circuit. Read on ... for this will be an important point to recognize as you begin to relate the battery voltage to the current and resistance.
Voltage-Current-Resistance
One of the most pervasive formulas in electricity is ∆V = I•R. The difference in electric potential between any two locations (∆V) is equal to the resistance of any devices located between those two locations multiplied by the current in the wire that connects those two locations. 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 second column (Resistance of Resistor 1, R1), and the fifth column (Current at Location B) can be related. And similarly, the first column (Battery Voltage), the third column (Resistance of Resistor 2, R2), and the sixth column (Current at Location C) can be related using the same equation. For each set of three columns, knowing two of the three columns allows you to calculate the third value.
Comparing Currents at Different Locations
The last four columns of the table have the headings - Current at A, Current at B, Current at C, and Current at D. Locations B and C are what we commonly refer to as branch locations. They represent locations inside of a branch that has a current that is distinctly different than the current outside of the branch as well as inside of the other branch. There is no reason to expect the current at Location B to be equal to the current at Location C. And one would never expect the current in the branches (at B or at C) to be equal to the current at Locations A or at Location D. But what you can expect is that the sum of the current in the branches equals the current outside of the branches. That is, IB + IC is equal to IA. And for the same reason, you can expect that IB + IC is equal to ID. This is because any charge that flows through Location B (resistor 1) will meet up with charge that flows through Location C and combine to form a new current value that then flows through Location D ... and also through Location A. And finally, since all the charge that flows through Location D also flows through Location A, you can expect that the current at these two locations are equal to each other.