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Chapter 12: Problem 1818

In the given circuit the equivalent resistance between the points \(\mathrm{A}\) and \(\mathrm{B}\) in \(\mathrm{ohm}\) is. (A) 9 (B) \(11.6\) (C) \(14.5\) (D) \(21.2\)

Short Answer

Expert verified
The equivalent resistance between points A and B in the given circuit is approximately \(11.667\, \Omega\). Thus, the correct answer is (B).

Step by step solution

01

Identify the layout of the circuit and the resistors connection

For the given circuit, the resistors are connected in a combination of series and parallel. We have to observe the circuit to determine the connections and simplify the resistors step by step.
02

Firstly, simplify the parallel connected resistors

In the circuit, we can see that there are some resistors connected in parallel. Let's simplify them using the parallel resistors formula: For the resistors \(R_1=14\) and \(R_2=7\), connected in parallel: \[\frac{1}{R_{eq1}} = \frac{1}{14} + \frac{1}{7}\]
03

Calculate the equivalent resistance for the parallel resistors

Now, let's calculate the equivalent resistance for \(R_{eq1}\) from the calculation above: \[\frac{1}{R_{eq1}} = \frac{1+2}{14} = \frac{3}{14}\] Therefore, \(R_{eq1} = 4.667\, \Omega\).
04

Next, simplify the series connected resistors

Now, we have the simplified circuit with resistors \(R_{eq1}\), \(R_3=5\), and \(R_4=2\) connected in series. Let's calculate the equivalent resistance using the series resistors formula: \[R_{eq} = R_{eq1} + R_3 + R_4\]
05

Calculate the overall equivalent resistance

Finally, let's find out the overall equivalent resistance: \[R_{eq} = 4.667 + 5 + 2 = 11.667\, \Omega\] The equivalent resistance between points A and B in the given circuit is approximately \(11.667\, \Omega\). Thus, the correct answer is (B).

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