Simple Urgent question: voltage for circuit

Question

A 6V battery, three resistors and three voltmeters are connected. What are the possible readings for each voltmeter?

My answer: 3V for top resistor, 3V for second resistor and 6V for the bottom resistor.

Actual answer: 2V each for the first two resistors and 4V for the bottom resistor. I do not understand why. Could I have detailed explanation? Thanks in advance. :)

      -/=R=/-

=[b]==      =======

      -/=R=/-    

====/=R=/=====

Description: in the above "circuit diagram", the R symbol represents a resistor which are of course connected into a circuit though not shown above. The top section with the two resistors are separated into one path for each resistor. The bottom resistor is on a straight wire as shown. [b] represents the battery.

Answer 1

The Voltage Rise of 6 Volts must equal the sum of the Voltage Drop across the Equivalent Resistance of the "top" 2 Resistors (which are in parallel) and the Voltage Drop across the "bottom" Resistor (which is in series with the Equivalent Resistance of the "top" 2 Resistors in parallel).

Number the 3 Resistors as R_1, R_2, & R₃ from "top" to "bottom".

The Equivalent Resistance of the 2 Resistors in parallel is given by R_eq = (R₁R₂)/(R₁ + R₂). The Total Current for this circuit is I = 6V/(R_eq + R₃).

Write 6V = IR_eq + IR₃. The Total Current I "splits" at the 2 parallel Resistors and the currents in R₁ and R₂ will only be equal if R₁ = R₂. However, the Voltage Drop across R₁ and R₂ is the same as the Voltage Drop across the Equivalent Resistance R_eq.

[Note also that I₁R₁ = IR_eq = R₁R₂I/(R₁ + R₂) or I₁ = R₂I/(R₁ + R₂); likewise, I₂ = R₁I/(R₁ + R₂). Adding these expressions for I₁ and I₂ will give a sum that simplifies to I.

Having been given no specific values for I,R₁, R₂, and R₃, it follows that V₁=I₁R₁ and V₂=I₂R₂, as well as V₃=I₃R₃=IR₃, cannot be determined.

Examining "your" answer and the "actual" answer, it can be seen that the Voltage Drops in the "actual" answer (V₁ = V₂ = V_eq = 2V and V₃ = 4V) do give a sum equal to the Voltage Rise supplied by the Circuit Battery; that is, 2V + 4V = 6V.

"Your" answer, however, gives a sum of Voltage Drops equal to 3V + 6V or 9V which does not equal the Voltage Rise of 6V supplied by the Circuit Battery.