class: center, middle # EE-281 ELECTRIC CIRCUITS ## Ozan Keysan [ozan.keysan.me](http://ozan.keysan.me) Office: C-113 <span class="meta">•</span> Tel: 210 7586 --- # Series Resistors <img src="http://upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Resistors_in_Series.svg/600px-Resistors_in_Series.svg.png" alt="Drawing" style="width: 600px;"/> ## $$R_{tot}=R_1+R_2+R_3 ... R_n$$ --- # Parallel Resistors <img src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/64/Resistors_in_Parallel.svg/600px-Resistors_in_Parallel.svg.png" alt="Drawing" style="width: 600px;"/> ## $$ \frac{1}{R_{tot}} = \frac{1}{R_1} + \frac{1}{R_2} ... + \frac{1}{R_n} $$ --- # Can you find the equivalent circuit?  -- ### You need one more tool! --- # Delta (\\(\Delta\\)) Connection: ### Two circuits are equivalent  --- #Wye (\\(Y\\)) Connection: ### Two circuits are equivalent  --- # (\\(\Delta - Y \\)) Transformation <img src=delta_wye.png alt="Drawing" style="width: 750px;"/> --- # (\\(\Delta - Y \\)) Transformation <img src=delta_wye.png alt="Drawing" style="width: 700px;"/> $$R_1=\frac{R_bR_c}{R_a + R_b + R_c}$$ $$R_2=\frac{R_aR_c}{R_a + R_b + R_c}$$ $$R_3=\frac{R_aR_b}{R_a + R_b + R_c}$$ --- # (\\(Y - \Delta \\)) Transformation <img src=delta_wye.png alt="Drawing" style="width: 700px;"/> $$R_a = \frac{R_1R_2 + R_2R_3+R_3R_1}{R_1}$$ $$R_b = \frac{R_1R_2 + R_2R_3+R_3R_1}{R_2}$$ $$R_c = \frac{R_1R_2 + R_2R_3+R_3R_1}{R_3}$$ --- # Example ### Find the equivalent Wye circuit.  --- # Quiz --- # Any questions? ## You can download this presentation from: [keysan.me/ee281](http://keysan.me/ee281)