Four resistance each of 8 ohm are connected to a square. The resistance between any two diagonally opposite terminals will be ?
16 each way
two 16 ohm resistors in parallel
1/R = 1/16 + 1/16 = 1/8
LOL, 8
To find the resistance between two diagonally opposite terminals of a square, we can use the concept of equivalent resistance.
Given that there are four resistors each with a resistance of 8 ohms connected to a square, we can label the resistors as follows:
R R
______ ______
| |
R| |
|______|
Let's label the four corners of the square as A, B, C, and D. Now, we can find the equivalent resistance between any two diagonally opposite terminals, say between A and C.
To simplify the calculation, we will first calculate the equivalent resistance between points A and B, and between points B and C. Then, we can add the two equivalent resistances together to get the total resistance between A and C.
1. Equivalent resistance between A and B:
In this case, resistor R on the top is connected in parallel with two resistors R on the sides (left and right). So, we can use the formula for resistors in parallel:
1/Req_AB = 1/R + 1/R + 1/R
1/Req_AB = 3/R
Req_AB = R/3
2. Equivalent resistance between B and C:
Here, the resistor R on the top is connected in series with two resistors R on the sides (left and right). So, we can use the formula for resistors in series:
Req_BC = R + R + R
Req_BC = 3R
3. Total resistance between A and C:
Since the resistors between A and B and between B and C are connected in series, we can add their equivalent resistances:
Req_AC = Req_AB + Req_BC
Req_AC = R/3 + 3R
Req_AC = (R + 9R)/3
Req_AC = 10R/3
Therefore, the resistance between any two diagonally opposite terminals (A and C in this case) will be 10 times the resistance of each individual resistor, which is 8 ohms.
Hence, the resistance between any two diagonally opposite terminals of the square will be 80 ohms.