Question

find the total resistance of the circuit.
5a
a 15ω
b 15ω
c 30ω
6 ohm
60 ohm
10 ohm
15 ohm

Explanation:

Step1: Identify Circuit Type

Resistors A, B, C are in parallel. Parallel resistance formula: $\frac{1}{R_{total}} = \frac{1}{R_A} + \frac{1}{R_B} + \frac{1}{R_C}$

Step2: Substitute Values

$R_A = 15\Omega$, $R_B = 15\Omega$, $R_C = 30\Omega$
$\frac{1}{R_{total}} = \frac{1}{15} + \frac{1}{15} + \frac{1}{30}$

Step3: Simplify the Sum

Find common denominator (30):
$\frac{2}{30} + \frac{2}{30} + \frac{1}{30} = \frac{5}{30} = \frac{1}{6}$

Step4: Find $R_{total}$

Take reciprocal: $R_{total} = 6\Omega$

Answer:

6 ohm