A circuit is constructed with five resistors and a battery a

A circuit is constructed with five resistors and a battery as shown. The values for the resistors are: R₁ = R₅ = 61 , R₂ = 106 , R₃ = 115 , and R₄ = 72 . The battery voltage is V = 12 V.

1)

What is R_ab, the equivalent resistance between points a and b?

2)

What is R_ac, the equivalent resistance between points a and c?

3)

What is I₅, the current that flows through resistor R₅?A

4)

What is I₂, the current that flows through resistor R₂?A

5)

What is I₁, the current that flows through the resistor R₁?A

6)

What is V₄, the voltage across resistor R₄?V

Solution

1) R_ab = (106 + 115) * 72 / [106 + 115 + 72]

= 54.31 ohms

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2) R_ac = 54.31 + 61

= 115.31 ohm

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3)  I₅ = V / (R_ac + R₅)

= 12 / (115.31 + 61) = 0.0681 A

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4) V_ab = I₅ x R_ab

I₂ = V_ab / (R₂ + R₃) = (I₅ x R_ab) / (R₂ + R₃) = (0.0681 x 54.31) / (106 + 115)

= 0.0167 A

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I₁ = I₅ = 0.0681 A

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V₄ = V_ab = I₅ x R_ab = 0.0681 * 54.31

= 3.69 A