Maximum voltage that can be applied to DC circuit with resistors

[Sokolov]

Homework Statement

In a DC circuit, two resistors $R_1$ and $R_2$ are connected in parallel, and a third resistor $R_3$ is connected in series with them, as shown in the picture. If the maximum power that each of these 3 resistors can hold is $P_{max}$, which would be the maximum voltage that could be applied between the points a and b?

Relevant Equations

Kirchhoff's laws: $I_1+I_2=I_3$
The power dissipated by a resistor: $P=I^2R=IV=V^2/R$

I see that $V_{ac}=V_{ab}+V_{bc}$, with $V_{ab}=I_1R_1=I_2R_2$ and $V_{bc}=I_3R_3$.

However, I don't see how to express mathematically the maximum value of $V_{ac}$. Could someone please help me with this task?

 

[BvU]

how to express mathematically the maximum value of $V_{ac}$

Can you do it with $V_{ab}$ or $V_{bc}$ ?

 

[Sokolov]

Can you do it with $V_{ab}$ or $V_{bc}$ ?

I think that the result must be given in terms of $P_{max}$. The exercise ask also to apply the result for the particular case that $R1=2.8 kΩ, R2=3.7 kΩ, R3=1.8 kΩ$ and $P_{max}=0.5W$

 

[BvU]

I agree, but you must start somewhere. Use $P_{\text {max}}$ and $R_i$ (as symbols).
How many equations witth how many unknowns do yuo have ? Do you have to distinguish cases ?

If the parallel circuit is annoying, use the equivalent resistance.