Question

MY NOTES

Electric current measures (in amperes or amps) the flow of electrons through wires. Like traffic flow, the current entering an intersection of wires must equal the current leaving it. Here is an
electrical circuit known as a Wheatstone bridge.
By measuring z, we can determine x, y, and w.
By measuring w, we can determine x, y, and z.
X
ASK YOUR TEACHER
(a) If the currents in two of the wires are a 18 amps and b-9 amps as shown, determine the currents in the other wires in terms of suitable parameters. (If there is no solution, enter NO
SOLUTION. If the system is dependent, express your answer using the parameters x, y, z, and/or w.)
(x, y, z, w) -
(b) Using the information obtained in part (a), in which wire should you measure the current in order to know all of the currents exactly? (Select all that apply.)
By measuring x, we can determine y, z, and w.
By measuring y, we can determine x, z, and w.
Need Help?
Read t
PRACTICE ANOTHER

Answer 1

Explanation:

(a) Since the current entering and leaving the intersection of wires must be equal, we have:

x + y = 18 (current entering the top intersection)

z + w = 18 (current leaving the top intersection)

x + z = 9 (current entering the bottom intersection)

y + w = 9 (current leaving the bottom intersection)

We can solve this system of equations using substitution or elimination. For example, we can eliminate w by adding the first two equations and subtracting the last two equations:

2x + 2y + 2z = 36

2y + 2z - 2x = 0

2z - 2x = 9

Solving for z in terms of x, we get:

z = (x + 9/2)

Substituting this into the first equation, we get:

x + y = 18

Substituting z in terms of x into the second equation, we get:

w = (18 - z) = (18 - x - 9/2) = (27/2 - x)

Therefore, the solution in terms of x, y, z, and w is:

(x, y, z, w) = (x, 18 - x, x + 9/2, 27/2 - x)

(b) To know all of the currents exactly, we need to measure the current in any one wire that is not already determined by the system of equations. From part (a), we see that w is determined in terms of x, y, and z. Therefore, we should measure the current in wire x or y to know all of the currents exactly.