Question

what is the total resistance in the circuit shown below?$r_1=3\\ \omegaLXB0r_3=5\\ \omega$9 v$circ$ 18.0$circ$ 15.0$circ$ 30.0$circ$ 16.0what is the total resistance shown in this circuit?$v=9\\ vLXB1r_2=2\omegaLXB2circ$ 0.625 0$circ$ 1.6 0$circ$ 0.625 0$circ$ 2.1 0

Explanation:

First Circuit (Series)

Step1: Identify series resistors

All resistors are in series, so total resistance is sum of $R_1$, $R_2$, $R_3$.

Step2: Calculate total resistance

$R_{total} = R_1 + R_2 + R_3 = 3\,\Omega + 10\,\Omega + 5\,\Omega$

Step1: Recall parallel resistance formula

For parallel resistors, $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$

Step2: Substitute resistor values

$\frac{1}{R_{total}} = \frac{1}{10\,\Omega} + \frac{1}{2\,\Omega} + \frac{1}{1\,\Omega} = 0.1 + 0.5 + 1 = 1.6$

Step3: Solve for total resistance

$R_{total} = \frac{1}{1.6} = 0.625\,\Omega$

Answer:

18 Ω (matches the second option: 18.0)

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Second Circuit (Parallel)