Electromagnetism - Kirchoff's Law

See Question #32. The voltage across resistor R₄ is

A. 0.4 V
B. 0.6 V
C. 1.2 V
D. 1.5 V
E. 3.0 V

(GR9277 #33)

Solution:

Parallel: V_t = V₁ = V₂ = V₃ = ...

Series: V_t = V₁ + V₂ + V₃ + ...

V₄ = V₃ = V₃₄
V₃₄ + V₅ = V₂ 
V₂ + V₁ = V_t 

Or, using Kirchoff's Law:
Loop 1: V_t  = V₁ + V₂  
Loop 2: V_t  = V₁ + V₃₄ + V₅

From Question #32:
R₃₄ = 20
R₃₄₅ = 50
R₂₃₄₅ = 25

R_t = R₁ + R₂₃₄₅ = 50 + 25 = 75
I_t = V_t / R_t = 3/75 = I₁
V₁ =  I₁ R₁ = (3/75) × 50 = 2

Thus, V₃₄ + V₅ = V_t −V₁ = 3 − 2 = 1

V₃₄ must be less than 1
Only (A) and (B) could be TRUE

Since R₄ = R₅ but R₄ is in parallel with R₃ → V₄ must be less than V₅ 

Answer: A

Complete Calculation:

I₁ =  I₂ + I₃₄₅

R₃₄₅ = 50 = R₂
I₃₄₅ = I₂ =  I₁ / 2 = (3/75) / 2 = 3/150

R₃₄ and R₅ are in series
I₃₄₅ = I₃₄ = I₅
V₄ = V₃₄ = I₃₄ R₃₄ = (3/150) × 20 = 60/150 = 0.4