예제 1-4 RL circuit 𝐿 𝑑𝐼 𝑑𝑡 +𝑅𝐼+ 1 𝐶 𝐼𝑑𝑡 = 𝑉 𝑠 (𝑡) 𝑰 𝒕 ? 𝐿 𝑑𝐼 𝑑𝑡 +𝑅𝐼+ 1 𝐶 𝐼𝑑𝑡 = 𝑉 𝑠 (𝑡) 예제 1-4 RL circuit 𝑰 𝒕 ? 𝑅𝐼+𝐿 𝑑𝐼 𝑑𝑡 = 𝑉 𝑠 (𝑡) 𝑣 𝑠 𝑡 ==5cos(𝜔𝑡) 𝑅𝑖+𝐿 𝑑𝑖 𝑑𝑡 =5 𝑒 𝑗𝜔𝑡 (𝜔=4∗ 10 4 ) 𝐼= 𝐼 𝑒 𝑗𝜔𝑡 , 𝑉 𝑠 𝑡 = 𝑉 𝑠 𝑒 𝑗𝜔𝑡 4. 𝐼 𝑅+𝑗𝜔𝐿 𝐼 = 𝑉 𝑠 5. 𝐼 = 𝑉 𝑠 𝑅+𝑗𝜔𝐿 = 5 6+𝑗8 = 5 6+𝑗8 = 5 10 𝑒 𝑗(53.1°) =0.5 𝑒 𝑗(− 53.1 ° ) 6. 𝐼(𝑡)=0.5 𝑒 𝑗(− 53.1 ° ) 𝑒 𝑗𝜔𝑡 7. 최종적인 답은 𝑅𝑒𝑎𝑙 𝐼 𝑡 =0.5cos(𝜔𝑡− 53.1 ° ) 𝑉 𝑡 =𝐿 𝑑𝑖 𝑑𝑡 =−4sin(𝜔𝑡− 53.1 ° )
RC circuit RLC circuit R=2 Ω 𝑰 𝒕 ? 1. 𝑅𝐼+ 1 𝐶 𝐼𝑑𝑡 = 𝑉 𝑠 (𝑡) 1. 𝑅𝐼+ 1 𝐶 𝐼𝑑𝑡 = 𝑉 𝑠 (𝑡) 𝑣 s = cos 4× 10 4 𝑡 C=1× 10 −4 (𝐹 𝐼= 𝐼 𝑒 𝑗𝜔𝑡 , 𝑉 𝑠 𝑡 = 𝑉 𝑠 𝑒 𝑗𝜔𝑡 2. 𝐼 𝑅+ 1 𝑗𝜔𝐶 𝐼 = 𝑉 𝑠 RLC circuit
𝐿 𝑑𝐼 𝑑𝑡 +𝑅𝐼+ 1 𝐶 𝐼𝑑𝑡 = 𝑉 𝑠 (𝑡) 𝐼 𝑅+𝑗𝜔𝐿 𝐼 + 1 𝑗𝜔𝐶 𝐼 = 𝑉 𝑠 𝐿 𝑑𝐼 𝑑𝑡 +𝑅𝐼+ 1 𝐶 𝐼𝑑𝑡 = 𝑉 𝑠 (𝑡) 𝐼 𝑅+𝑗𝜔𝐿 𝐼 + 1 𝑗𝜔𝐶 𝐼 = 𝑉 𝑠 𝐓𝐡𝐞 𝐢𝐦𝐩𝐞𝐝𝐚𝐧𝐜𝐞 ? 𝑍: the impedance 𝐼 = 𝑉 𝑠 1 𝑗𝜔𝐶 +𝑗𝜔𝐿+𝑅 = 𝑉 𝑠 𝑍 𝑍= 1 𝑗𝜔𝐶 +𝑗𝜔𝐿+𝑅 = 𝑍 𝑒 𝑗𝜙 𝐼= 𝐼 𝑒 𝑗𝜔𝑡 = 𝑉 𝑠 𝑍 𝑒 𝑗𝜔𝑡 = 𝑉 𝑍 𝒁 = 𝑹 𝟐 + 𝑳𝝎− 𝟏 𝝎𝑪 𝟐 𝐼= 𝑉 𝑍 = 𝑉 𝑍 𝑒 −𝑗𝜙 𝐼 𝑟 𝑡 =R𝑒[ 𝑉 𝑠 𝑍 𝑒 𝑗𝜔𝑡 ] 𝐭𝐚𝐧 𝝓 = (𝑳𝝎−𝟏/𝛚𝐂) 𝑹 𝐼 𝑟 𝑡 =R𝑒 𝑉 0 𝑍 𝑒 𝑗 𝜔𝑡−𝜙 = 𝑉 0 𝑍 cos(𝜔𝑡−𝜙) Resonance (공명) 𝝎= 1 𝐿𝐶 𝝎 커지면 𝝓?