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Bài 1:
a, \(\)\(\)\(=>R2//\left[R4nt\left(R3//R5\right)\right]\)
\(=>Rtd=\dfrac{R2\left[R4+\dfrac{R3.R5}{R3+R5}\right]}{R2+R4+\dfrac{R3.R5}{R3+R5}}=\dfrac{1.\left[1+\dfrac{1}{1+1}\right]}{1+1+\dfrac{1}{1+1}}=0,6\left(ôm\right)\)
\(=>I=\dfrac{Uab}{Rtd}=\dfrac{10}{0,6}=\dfrac{50}{3}A=I1\)
\(=>Uab=U2345=10V=U2=U345\)
\(=>I2=\dfrac{U2}{R2}=\dfrac{10}{1}=10A\)
\(=>I345=\dfrac{U345}{R345}=\dfrac{10}{1+\dfrac{1.1}{1+1}}=\dfrac{20}{3}A=I4=I35\)
\(=>U35=I35.R35=\dfrac{20}{3}.\dfrac{1.1}{1+1}=\dfrac{10}{3}V=U3=U5\)
\(=>I3=\dfrac{U3}{R3}=\dfrac{\dfrac{10}{3}}{1}=\dfrac{10}{3}A,\)
\(=>I5=\dfrac{U5}{R5}=\dfrac{10}{3}A\)
b, \(I1=0,1A=Im=I2345\)
\(=>Uab=I2345.R2345=0,1.\dfrac{6\left[8+\dfrac{6.12}{6+12}\right]}{6+8+\dfrac{6.12}{6+12}}=0,4V\)
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Bài 3:
a. \(R=R1+R2=15+30=45\Omega\)
b. \(\left\{{}\begin{matrix}I=U:R=9:45=0,2A\\I=I1=I2=0,2A\left(R1ntR2\right)\end{matrix}\right.\)
c. \(\left\{{}\begin{matrix}U1=R1.I1=15.0,2=3V\\U2=R2.I2=30.0,2=6V\end{matrix}\right.\)
Bài 4:
\(I1=U1:R1=6:3=2A\)
\(\Rightarrow I=I1=I2=2A\left(R1ntR2\right)\)
\(U=R.I=\left(3+15\right).2=36V\)
\(U2=R2.I2=15.2=30V\)
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a)\(R_b=\dfrac{U^2_b}{P_b}=\dfrac{220^2}{1500}=\dfrac{484}{15}\Omega\)
\(I=\dfrac{U}{R}=\dfrac{220}{\dfrac{484}{15}}=\dfrac{75}{11}A\)
b)Điện năng bếp tiêu thụ trong 30 ngày:
\(A=UIt=220\cdot\dfrac{75}{11}\cdot30\cdot1,5\cdot3600=8100000J=2,25kWh\)
Số đếm công tơ điện là 2,25 số điện.
c)Nhiệt lượng càn thiết để đun sôi 2l nước:
\(Q_{thu}=mc\Delta t=2\cdot4200\cdot\left(100-30\right)=588000J\)
\(H=\dfrac{Q_{thu}}{A}=75\%\)
\(\Rightarrow UIt=A=\dfrac{Q_{thu}}{H}=\dfrac{588000}{75\%}=784000J\)
\(\Leftrightarrow t=\dfrac{784000}{220\cdot\dfrac{75}{11}}=522,67s\)
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\(R_{tđ}=\dfrac{R_1\cdot R_2}{R_1+R_2}=\dfrac{24\cdot12}{24+12}=8\Omega\)
\(I=\dfrac{U}{R}=\dfrac{12}{8}=1,5A\)
\(P=\dfrac{U^2}{R}=\dfrac{12^2}{8}=18W\)
\(Q_{tỏa1}=A_1=U_1\cdot I_1\cdot t=12\cdot\dfrac{12}{24}\cdot1\cdot3600=21600J\)
\(Q_{tỏa2}=A_2=U_2\cdot I_2\cdot t=12\cdot\dfrac{12}{12}\cdot1\cdot3600=43200J\)
ta có:
khi khóa k ngắt:
R2 nt R3
Uv=U3=6V
\(\Rightarrow I_3=\frac{U_3}{R_3}=1.2A\)
mà I3=I2 nên I2=1.2A
U=U2+U3
\(\Leftrightarrow U=I_2R_2+I_3R_3=1.2R_2+6\left(1\right)\)
khi khóa k đóng
R3 nt (R1//R2)
Uv=U3=8V
\(\Rightarrow I_3=\frac{U_3}{R_3}=1.6A\)
\(\Rightarrow I_1+I_2=1.6A\)
\(\Leftrightarrow\frac{U_1}{R_1}+\frac{U_2}{R_2}=1.6\)
\(\Leftrightarrow\frac{U_1}{10}+\frac{U_2}{R_2}=1.6\)
mà U1=U2 nên:
\(\frac{U_1}{10}+\frac{U_1}{R_2}=1.6\)
\(\Leftrightarrow\frac{U_1R_2+10U_1}{10R_2}=1.6\)
\(\Leftrightarrow U_1\left(R_2+10\right)=16R_2\)
\(\Rightarrow U_1=\frac{16R_2}{R_2+10}\left(2\right)\)
ta lại có:
U=U3+U1
\(\Leftrightarrow U=8+U_1\)
thế (2) vào phương trình trên ta có:
\(U=8+\frac{16R_2}{R_2+10}\)
\(\Leftrightarrow U=\frac{8R_2+80+16R_2}{R_2+10}\)
\(\Leftrightarrow U=\frac{24R_2+80}{R_2+10}\left(3\right)\)
do U không đổi nên ta có:
(1)=(3)
\(\Leftrightarrow1.2R_2+6=\frac{24R_2+80}{R_2+10}\)
\(\Leftrightarrow\left(1.2R_2+6\right)\left(R_2+10\right)=24R_2+80\)
\(\Leftrightarrow1.2R^2_2+6R_2+12R_2+60=24R_2+80\)
\(\Leftrightarrow1.2R^2_2-6R_2-20=0\)
giải phương trình ta có:
R2=7.3Ω (loại R2=-2.3Ω do âm)
\(\Rightarrow U=14.76V\)