Electric Circuits and Electrical Concepts (Lecture Notes)

A comprehensive set of questions and answers covering current, charge, drift velocity, resistance, Ohm’s law, resistivity, circuit laws, series/parallel circuits, EMF vs PD, diodes, and power. Designed to review key concepts from the lecture notes.

What is the definition of electric current?

The flow of charge per unit time. Symbol: I. SI unit: Ampere (A). It is I = Q/t or Q = I t.

What is a Coulomb and how is it defined?

Coulomb (C) is the SI unit of charge. It is the charge transferred when a current of 1 A passes through a point for 1 s. 1 C = 1 A·s; e (elementary charge) ≈ 1.6×10^-19 C.

Under what condition can you use Q = It to find charge?

When the current is constant. If the current is changing, Q = It cannot be applied directly.

What does the area under an I–t graph represent?

The charge transferred. For constant current, the area is a rectangle (I×t). For changing current, the area under the curve gives Q.

In which direction does conventional current flow relative to a circuit’s terminals?

From the positive to the negative terminal. Electrons move from negative to positive.

What is drift velocity?

The average velocity of free charge carriers (electrons) as they move through a conductor under an electric field.

Give the formula that relates current to drift velocity.

I = n e A vd, where n is electron density, e is elementary charge, A is cross-sectional area, and vd is drift velocity.

How do you calculate cross–sectional area for a wire with circular cross-section?

A = πr^2 = (πd^2)/4, where d is the diameter and r is the radius.

What does Ohm’s law state for an ohmic conductor?

Voltage is proportional to current (V ∝ I) with constant resistance. In form: V = IR; R = V/I. The relation holds when temperature and geometry remain constant.

What is resistivity and how is it used to calculate resistance?

Resistivity (ρ) is an intrinsic property of a material. R = ρL/A for a conductor of length L and cross-sectional area A.

How does resistance depend on length and cross-sectional area?

Resistance increases with length (R ∝ L) and decreases with cross-sectional area (R ∝ 1/A). For a given material, R = ρL/A.

What are typical qualitatively different ranges of resistivity by material type?

Conductors have very low resistivity, semiconductors have intermediate resistivity, and insulators have very high resistivity.

How does temperature generally affect resistance in conductors?

Resistance usually increases with temperature for most conductors.

If R is plotted against length L, what does the gradient represent?

Gradient = ρ/A. Therefore, ρ = (gradient) × A. A can be found from geometry (A = πr^2 or πd^2/4).

What is a fixed resistor and what is a variable resistor?

Fixed resistor provides a single fixed resistance. Variable resistor (rheostat) provides a range of resistances.

How does a Light-Dependent Resistor (LDR) respond to light?

Resistance decreases as light intensity increases.

How does a Thermistor behave with temperature?

Resistance decreases with increasing temperature for a typical thermistor (NTC). The resistance is temperature-dependent.

What is a diode and what does a PN junction do?

A diode is a PN junction that allows current to pass mainly in one direction (forward bias) and blocks current in reverse bias.

What happens in forward bias and reverse bias for a diode?

Forward bias: current can pass. Reverse bias: current is blocked (diode acts like an open switch). Large reverse bias can lead to breakdown.

What is EMF (electromotive force) vs potential difference (PD)?

EMF is the energy supplied per unit charge around a complete loop (source). PD is the energy per unit charge across the external circuit (terminal PD). Emf accounts for internal resistance; PD across the external circuit is V. Emf = Vexternal + Vinternal.

How is EMF measured and how does a voltmeter reading differ when the circuit is open or closed?

A voltmeter measures potential difference. Across an unloaded source (open circuit), it can read EMF. When the external circuit is connected (load present, switch closed), it reads the terminal PD, not the EMF.

What is the relationship E = IR + Ir?

EMF (E) equals the sum of the external voltage drop IR (across external resistance) plus the internal drop I r (inside the source).

What is electrical power and its common formulas?

Power P is energy transferred per unit time. P = VI = I^2R = V^2/R. In energy form, E = Pt; E = VI t; and E = VQ.

What does Kirchhoff’s Current Law (KCL) state?

At any junction, the sum of currents entering the junction equals the sum of currents leaving the junction.

What does Kirchhoff’s Voltage Law (KVL) state?

In a closed loop, the sum of emfs equals the sum of potential drops across components; based on conservation of energy.

How do you calculate total resistance in series and in parallel?

Series: RT = R1 + R2 + …; Current is the same through all components. Parallel: 1/RT = 1/R1 + 1/R2 + …; Voltages are the same across all branches; Currents add.

If a circuit has two resistors in series and a total voltage V_in, how do you find the current through the circuit?

I = Vtotal / Rtotal, where R_total = R1 + R2 for the series branch.

How is voltage divided among components in series?

Voltage across each component is proportional to its resistance: Vi = I Ri. For two resistors, Vout across R1 is Vin × R1/(R1+R2).

How is current distributed in parallel branches?

Branch current Ii = V / Ri. The total current Itotal is the sum of all branch currents: Itotal = I1 + I2 + I3 + … .

What is the significance of a junction in circuit analysis?

A junction is a point where the circuit splits into branches; used in applying KCL.

What are the signs rules when applying Kirchhoff’s loop equations?

Choose a loop direction. If the loop direction aligns with the direction of a component’s current, use a positive sign for that drop; if opposite, use a negative sign. Keep the loop direction and elements fixed once chosen.

What is meant by a potential divider?

A configuration (usually series) where the output voltage across one component (or a combination) varies as a function of resistance and input EMF; used to obtain different voltages.

What is meant by the area under a current–time graph if current changes?

It represents the total charge transferred, Q = ∫ I dt. If the current is constant, Q = I t.

What is the relationship between current density and drift velocity?

In the formula I = n e A vd, the current density J = I/A = n e vd (for a given cross-section). Drift velocity is the average velocity of charge carriers.

How do you compute resistivity from a R–L graph?

Plot resistance R against length L. The slope m = dR/dL = ρ/A. Therefore ρ = m × A, where A is cross-sectional area.

What is meant by the term ‘internal resistance’ of a power supply?

The resistance inside the source itself. It causes a voltage drop Ir; EMF = Vexternal + Vinternal, and the external PD is V = IRext, while E = I(Rext + r).

What is the key difference between ohmic and non-ohmic conductors?

Ohmic conductors obey Ohm’s law with a straight-line V–I graph (constant resistance). Non-ohmic conductors show a curved V–I relationship (resistance changes with voltage, current, temperature, etc.).

How does a line from origin help in analyzing a non-ohmic conductor’s V–I graph?

For non-ohmic conductors, a straight line from origin to a given point can be used to determine the instantaneous resistance at that point as R = V/I, avoiding issues with a tangent that would introduce an intercept.

What is the general direction of current in an external circuit element and the role of sign conventions in loop equations?

Direction of current is determined by the actual current flow. In loop equations, signs depend on the relative directions of the loop and the current; maintain consistent loop orientation and mark signs accordingly.

What is the forward bias condition for a PN junction diode?

Forward bias allows current to pass through the diode; reverse bias blocks current (acts like an open switch except for breakdown conditions).

What is the difference between terminal PD and EMF in a circuit?

Terminal PD is the potential difference across the external circuit (load). EMF is the energy supplied per unit charge by the source, accounting for internal resistance; E = Vexternal + Vinternal.

What equation expresses power in terms of current and resistance?

P = I^2 R. Similarly, P = V^2 / R and P = VI.

What is the definition of potential difference in the context of circuits?

The work done per unit charge to move the charge between two points so as to drive the current through the circuit; in practice, the voltage between two points is the potential difference.