What is the magnitude of the potential difference across the 5- resistor?

Refer to the circuit diagram below.

Equivalent resistance for the three 10-ohm resistors]
= (10 + 10 + 10) Ω
= 30 Ω

Equivalent resistance across ab
= (30 × 20) / (30 + 20) Ω
= 12 Ω

Equivalent resistance of the whole circuit
= (5 + 12) Ω
= 17 Ω

Circuit of the main circuit, I
= V/R
= 11/17 A
= 0.647 A

Potential across the 5-Ω resistor, V
= IR
= 0.647 × 5 V
= 3.2 V

(10+10+10) = 30 ohm register  (all connected in series) is connected to 20 ohm in parallel.
so, the resultant resistor is: 1/R = 1/20 + 1/30 = 5/60= 1/12 ohms Hence,  R = 12 ohmsso now the given circuit consists of only 5 ohm resistor and 12 ohm resistor and of course including  the battery of 11 V (as given) .Now suppose the current passing through those 2 resistors is I Amp then11 - RI - 5I = 0 or 11 = RI+5I or 11 = I(12+5) = I*17 or  I = 11/17 ampHence, Potential difference across the register of 5 ohm will be:(U = RI) U = 5 * (11/17) = 55/17 = 3.24 Volts <= ans

The three 10 ohm resistors are in series.
Now the 30 and 20 ohm resistors are in parallel so their equivalent resistance is 20*30 / (20+30) = 12 ohms
Now the 12 and 5 ohm resistors are in series so the voltage on the 5 ohm resistor is 11 * 5 / (12+5) V