is a key point. When two resistors of the same

value are connected in parallel, the resultant

equivalent resistance is 1/2 the value of the

resistance of one of them. So, if you connect

two 80Ω resistors in parallel, the resistance

of that is 40Ω.

The formula: Voltage = Current * Resistance

or E=IR will be used in solving these problems.

You are given the current (I) through and

voltage or potential difference (E) across X.

(a) i – The current through X is the maximum

current in the circuit. Thus 0.8A is going

through the combination of Y and Z. Since

they are of equal value, 1/2 this current

goes through each. Thus Y carries 0.4A.

(a) ii – Since Z = Y, it carries the same

current which is 0.4A as well.

Note, if Y and Z were different values, the

current would be inversely proportional to

the resistance. The highest would have less

than the lowest resistor.

Do (c) Next:

You have to return to X for this and put

in the values provided to find the actual

resistance of X. Using E=IR: 1.6V = 0.8A * R.

Solving: R = 1.6/.8 = 2Ω.

Now we know the values of all resistors.

Remember that Y and Z are both 2Ω but are

in parallel so the equivalent value is 1Ω.

Now we know the values of all resistors.

The total resistance of the circuit is

3Ω (which answers (d)) and the total circuit

current is 0.8A (given)

Applying E=IR to get E = 0.8A*3Ω = 2.4 Volts.

(b) – The potential across Y is the same as

that across Z. Treat them as the single resistor.

There is no more voltage in the circuit than

the total. Since X drops 1.6V (given), then

the combination of YZ must be the remainder of

the source – X or: 2.4V – 1.6V = 0.8V

If you need the formulas to prove the parallel

resistance solution, let me know.