Total Resistance
A circuit contains four resistors in parallel: 3Ω, 6Ω, 9Ω, and 9Ω. Determine the total resistance in Ohms.
Expand Hint
For resistors connected in parallel, the voltage drop across each resistor is equivalent.
Hint 2
$$$R_{parallel}=\frac{1}{(1/R_1)+(1/R_2)+...+(1/R_n)}$$$
For resistors connected in parallel, the voltage drop across each resistor is equivalent. Therefore, the resistance of
$$n$$
resistors in parallel is:
$$$R_{parallel}=\frac{1}{(1/R_1)+(1/R_2)+...+(1/R_n)}$$$
Thus,
$$$R_{parallel}=\frac{1}{(1/3\Omega)+(1/6\Omega)+(1/9\Omega)+(1/9\Omega)}$$$
$$$R_{parallel}=\frac{1}{(12/36\Omega)+(6/36\Omega)+(4/36\Omega)+(4/36\Omega)}$$$
$$$R_{parallel}=\frac{1}{(26/36\Omega)}=\frac{36}{26}\Omega=1.38\: \Omega$$$
1.38 Ω
Time Analysis
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