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Answer (1)
[tex]\begin{gathered}\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\\end{gathered}\end{gathered}[/tex] To solve the problem with the parallel circuit containing three resistors (R₁, R₂, and R₃) connected to a 12V battery, we will follow these steps: Given: Voltage (V) = 12VResistors:R₁ = 10Ω R₂ = 15ΩR₃ = 30Ω Find the total resistance of the circuit. In a parallel circuit, the total resistance ([tex]R_t[/tex]) can be calculated using the formula: [tex]\frac{1}{R_t} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}[/tex] Substituting the values: [tex]\frac{1}{R_t} = \frac{1}{10} + \frac{1}{15} + \frac{1}{30}[/tex] To calculate this, we first find a common denominator. The least common multiple of 10, 15, and 30 is 30. Rewriting each term gives us: [tex]\frac{1}{10} = \frac{3}{30}, \frac{1}{15} = \frac{2}{30}, \frac{1}{30} = \frac{1}{30}[/tex] Now substituting these values into the equation: [tex]\frac{1}{R_t} = \frac{3}{30} + \frac{2}{30} + \frac{1}{30} = \frac{6}{30}[/tex] So, [tex]R_t = \frac{30}{6} = 5 \Omega[/tex] Calculate the total current supplied by the battery. Using Ohm's Law, the total current ([tex]I_t[/tex]) supplied by the battery can be calculated using the formula: [tex]I_t = \frac{V}{R_t}[/tex] Substituting the values: [tex]I_t = \frac{12V}{5 \Omega} = 2.4A[/tex] Determine the current flowing through each resistor. In a parallel circuit, the voltage across each resistor is the same as the voltage of the battery. Therefore, the current through each resistor can be calculated using Ohm's Law: [tex]I = \frac{V}{R}[/tex] Calculating the current through each resistor: For R₁:[tex]I_1 = \frac{12V}{10 \Omega} = 1.2A[/tex]For R₂:[tex]I_2 = \frac{12V}{15 \Omega} = 0.8A[/tex]For R₃:[tex]I_3 = \frac{12V}{30 \Omega} = 0.4A[/tex] Summary of Results: Total resistance of the circuit: [tex]R_t = 5 \Omega[/tex]Total current supplied by the battery: [tex]I_t = 2.4A[/tex]Current through each resistor: [tex]I_1 = 1.2A[/tex] [tex]I_2 = 0.8A[/tex] [tex]I_3 = 0.4A[/tex] [tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\begin{gathered} \boxed{\begin{array}{cc} \sf \footnotesize \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ···\: ʚ\: \: \: \: \: \: Hope\:it\:helps \: \: \: \: \: ɞ \:··· \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\footnotesize\:\# CarryOnLearning \\ \sf\footnotesize ૮₍´˶ \: • \: . \: • \: ⑅ ₎ა \: \leadsto \footnotesize\sf\color{purple} \underline{Study\:Well!}\end{array}}\end{gathered}[/tex][tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\large\qquad\qquad\qquad\tt MARCH/13/2025 [/tex]
