ECE 221 Electric Circuit Analysis I Chapter 4 Circuit Elements Herbert G. Mayer, PSU & CCUT Status 10/3/2015 Taken with permission from PSU Prof. Phillip Wong

Syllabus Resistor Inductor Capacitor Voltage and Current Sources Voltage and Current Dividers

Resistor A resistor is a passive electronic component that obeys Ohm’s Law. It has resistance R SI Unit: ohm () Symbol: Impedance: I-V relationship: R i(t) v(t)

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Resistors Connected in Series (end-to-end) If N resistors are connected in series, with the i-th resistor having a resistance Ri , then the equivalent resistance Req is:  R1 R2 Req = R1 + R2  Req = R1 + R2 + R3 R1 R2 R3

→ Iout Properties of Serial Resistances (DC): The amount of current Iin entering one end of a series circuit is equal to the amount of current Iout leaving the other end. The current is the same through each resistor in the series and is equal to Iin. Iin = Iout = I1 = I2 = I3 → I1 Iin → → I2 → I3 → Iout R1 R2 R3

The amount of voltage drop across each resistor in a series circuit is given by Ohm’s Law. V1 = IR1 , V2 = IR2 , V3= IR3 By convention, the resistor terminal that the current enters is labeled “+”, and the terminal the current exits is labeled “–” + – V1 I → → I + – V2 + – V3 R1 R2 R3

Example: 2  6  3  I VAB = 3 V Solution: Calculate the current I that flows through the resistors. Find the voltage drop across the 6  resistor. Assume 3 significant figures. Solution: a) Approach – Use Ohm’s law: Calculate the equivalent resistance: Calculate the current: b) Use Ohm’s law again:

Resistors Connected in Parallel (side-by-side) If N resistors are in parallel, with the i-th resistor having a resistance Ri , then the equivalent resistance is:  R1 R2  R3 R1 R2

Properties of Parallel Resistances (DC): The amount of current Iin entering one end of a parallel circuit is equal to the amount of current Iout leaving the other end For parallel resistors, the voltage drop across each resistor is the same Iin = Iout and V1 = V2 = V3 Iin → → Iout + V1 – R3 R1 R2 + V2 – + V3 –

The amount of current through each resistor in a parallel circuit is given by Ohm’s Law. The sum of the currents through each resistor is equal to the original amount of current entering or leaving the parallel circuit I1 + I2 + I3 = I I → → I + V – R3 R1 R2 I1 I2 I3 I1 = V / R1 I2 = V / R2 I3 = V / R3

Example: 2  Ix I = 4 A 6  3  VAB Solution: Find the current Ix through the 2  resistor. What is the power dissipated by the 3  resistor? Assume 3 significant figures. I = 4 A 6  A B 3  VAB Solution: a) Approach – Use Ohm’s law: Calculate the equivalent resistance: Calculate the voltage drop: Find the current: b) Use power equation:

Inductor & Capacitor An inductor is a passive component that stores energy within a magnetic field. It has inductance L SI unit: henry (H) Impedance: Symbol: A capacitor is a passive component that stores energy within an electric field. It has capacitance C SI unit: farad (F) Impedance: polarized + non-polarized

DC Voltage & Current Sources An ideal DC voltage source outputs a constant voltage regardless of the amount of current through it + – Vs I An ideal DC current source outputs a constant current regardless of the amount of voltage across it Is V

Voltage & Current Dividers Voltage Divider R2 I R1 + – V0 V1 V2 Current Divider I + – VS G2 G1 I1 I2 14

What is the voltage drop across Ra? Example: What is the voltage drop across Ra? What is the voltage drop across Rb? Ra = 1 Ω Va Vs = 8 V + – Rb = 3 Ω Vb 15

Example: The voltage Vg from a signal generator must be reduced by a factor of three before entering an audio amplifier. Determine the resistor values of a voltage divider that performs this task R2 R1 Vg Vout Signal Generator Audio Amplifier Peak output = 3 V Max input = 1 V 16