Đáp án:
Giải thích các bước giải:
Mạch dạng R1 // (R2 nt R3)
Rtđ = $\frac{R1 . (R2 + R3)}{R1 + R2 + R3}$ = $\frac{12 . (15 + R3)}{12 + 15 + R3}$ = $\frac{180 + 12R3}{27 + R3}$
U1 = U23 = U = I.Rtđ = 2 . $\frac{180 + 12R3}{27 + R3}$ = $\frac{360 + 24R3}{27 + R3}$ (V)
I1 = $\frac{U1}{R1}$ = $\frac{360 + 24R3}{27 + R3}$ : 12 = $\frac{30 + 2R3}{27 + R3}$ (A)
U2 = U - U3 = $\frac{360 + 24R3}{27 + R3}$ - 3,75 (V)
I2 = $\frac{U2}{R2}$ = ($\frac{360 + 24R3}{27 + R3}$ - 3,75) : 15 = $\frac{24 + 1,6R3}{27 + R3}$ - 0.25 (A)
I = I1 + I2
⇔ $\frac{30 + 2R3}{27 + R3}$ + $\frac{24 + 1,6R3}{27 + R3}$ - 0.25 = 2
⇔ 30 + 2R3 + 24 + 1,6R3 = 2,25.(27 + R3)
⇔ 3,6R3 - 2,25R3 = 60,75 - 54
⇔ 1,35R3 = 6,75
⇔ R3 = 5