Hi Four resistors are connected to a battery as shown in the

Hi!

Four resistors are connected to a battery as shown in the figure below. (a) Determine the current in each resistor in terms of epsilon. (Use the following as necessary: for epsilon = (b) Determine the current in each resistor in terms of I. (Use the following as necessary: I.)

Solution

R_s = R₂ + R₃ are in parallel

Because V₄ = V_s = V₂ + V₄, voltage V₄ across R₄ > V₂ or V₃.

Equivalent resistance of R₄ and R_s in parallel

Rp = 1 / [1/R₄ + 1/R_s] = 1 / [1/3R + 1/6R] = 2 R

I = V_A / R_A = V_B / R_B

Rp = 2 R₁, So V₁ = Vp / 2, R₃ = 2 R₂, So V3 = 2 V₂

V₃ + V₂ = Vp, V₃ = 2/3 Vp, V₂ = Vp / 3

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E = V₁ + V_p = 3 V_p / 2

delta V₁ = V_p / 2 = E / 3

delta V₂ = V_p / 3 = 2 E / 9

delta V₃ = 2 V_p / 3 = 4 E / 9

delta V₄ = V_p = 2E / 3

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I = I₂ + I₃ , I is greate than I₂ and I₃

R₄ = 3 R < R_s = 6 R

I = V₁ / R₁ = (E/3) (1/R) = E / 3 R

I₃ = V_p / R₄ = (2E/3) (1/3 R) = 2 I / 3

I₂ = V_p / R_s = (2 E/3) (1/6R) = I / 3