Equivalent resistance of the following circuit (in ohms) is equal to \(\frac{x}{7}\). Value of x is equal to _____.
Equivalent resistance of the following circuit (in ohms) is equal to \(\frac{x}{7}\). Value of x is equal to _____.
Correct Answer: 16
Solution and Explanation
Let's analyze the circuit step-by-step to calculate the equivalent resistance between points A and B.
- Simplify the top two resistors: The two 8-ohm resistors are in series. Their combined resistance is 8 Ω + 8 Ω = 16 Ω.
- Simplify the two 4-ohm angled resistors: The two 4-ohm resistors connected to the terminals of 8 ohm resistors are also in series. The combined resistance is 4 Ω + 4 Ω = 8 Ω.
- Simplify the three 4-ohm and combined resistors: The combined 16-ohm resistor, the combined 8-ohm resistor and the 4-ohm resistor are connected in parallel. The formula for parallel resistors is 1/Req = 1/R1 + 1/R2 + 1/R3 , so, 1/Req = 1/16 + 1/8 + 1/4= (1+2+4)/16 = 7/16 The equivalent resistance is Req =16/7
Given that the equivalent resistance is x/7 ohms and calculated equivalent resistance is 16/7, so the value of x is 16.
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