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).