3. Three capacitors with capacitances 5 μF, 10 μF and 15 μF are connected in parallel. Find the capacitance of the combination. If they are connected to a battery of 240 V, find the charge in each capacitor.
4. Three capacitors with capacitances 4 μF, 8 μF, and 12 μF are connected in series. A voltage of 400 V is applied to the combination. (a) Find the charge in each capacitor. (b) What is the voltage across each capacitor?
with solution thank you!
3.
"C=C_1+C_2+C_3=5+10+15=30\\:\\rm \\mu F""q_1=C_1V=5*10^{-6}*240=1.2*10^{-3}\\:\\rm C"
"q_2=C_2V=10*10^{-6}*240=2.4*10^{-3}\\:\\rm C"
"q_3=C_3V=15*10^{-6}*240=3.6*10^{-3}\\:\\rm C"
4.
"\\frac{1}{C}=\\frac{1}{C_1}+\\frac{1}{C_2}+\\frac{1}{C_3}""\\frac{1}{C}=\\frac{1}{5\\:\\rm \\mu F}+\\frac{1}{10\\:\\rm \\mu F}+\\frac{1}{15\\:\\rm \\mu F}=0.367""C=2.73\\:\\rm \\mu F""q_1=q_2=q_3=CV\\\\\n=2.73*10^{-6}*400=1.09*10^{-3}\\rm C"
"V_1=\\frac{q_1}{C_1}=\\frac{1.09*10^{-3}}{5*10^{-6}}=218\\rm \\: V"
"V_2=\\frac{q_2}{C_2}=\\frac{1.09*10^{-3}}{10*10^{-6}}=109\\rm \\: V"
"V_3=\\frac{q_3}{C_3}=\\frac{1.09*10^{-3}}{15*10^{-6}}=73\\rm \\: V"
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