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The circuit to the right consists of a battery ( V 0 = 20.5 V) and five resistors ( R 1 = 411 Ω, R 2 = 282 Ω, R 3 = 463 Ω, R 4 = 434 Ω, and R 5 = 165 Ω). Find the current passing through each of the specified points.

User Hung Tran
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Final answer:

The current passing through each specified point in the circuit can be found by calculating the equivalent resistance and using Ohm's law. The current passing through R₁ and R₂ is 0.0294 A, the current passing through R₃ and R₄ is 4.10 A, and the current passing through R₅ is 0.124 A.

Step-by-step explanation:

In the given circuit, the battery has a voltage of V0 = 20.5 V and there are five resistors with resistance values R₁ = 411 Ω, R₂ = 282 Ω, R₃ = 463 Ω, R₄ = 434 Ω, and R₅ = 165 Ω.

To find the current passing through each specified point in the circuit, we need to calculate the equivalent resistance of the circuit and use Ohm's law (V = I × R) to determine the current. First, we can simplify the circuit by combining resistors R₃ and R₄ in parallel, which gives us an equivalent resistance of R₃₄ = (10.00 Ω × 52) / (10.00 Ω + 52) = 5.00 Ω.

Next, we can combine resistors R₁, R₂, and R₃₄ in series to obtain the equivalent resistance of the entire circuit, which is Req = R₁ + R₂ + R₃₄ = 411 Ω + 282 Ω + 5.00 Ω = 698 Ω.

Finally, we can use Ohm's law to find the current passing through each specified point. The current passing through R₁ and R₂ is the same, and it can be calculated as I = V0 / Req = 20.5 V / 698 Ω = 0.0294 A (rounded to four decimal places). The current passing through R₃ and R₄ (since they have the same resistance) can be calculated as I = V0 / R34 = 20.5 V / 5.00 Ω = 4.10 A (rounded to two decimal places).

Finally, the current passing through R5 can be calculated as I = V0 / R5 = 20.5 V / 165 Ω = 0.124 A (rounded to three decimal places).

User Warrick
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