Electromagentic , Mid-term 2 , questions

In an RC circuit during charging, the voltage across the capacitor is given by:

• V(t) = V0(e^(t/RC))

• V(t) = V0(1 - e^(-t/RC))

• V(t) = V0(1 + e^(-t/RC))

• V(t) = V0(e^(-t/RC))

Answer explanation

In an RC circuit, during charging, the voltage across the capacitor is described by V(t) = V0(1 - e^(-t/RC)). This equation shows how the voltage approaches V0 as time increases, making it the correct choice.

The time constant (τ) of an RC circuit is:

• τ = R × C

• τ = C / R

• τ = R / C

• τ = R + C

Answer explanation

The time constant (τ) of an RC circuit is defined as τ = R × C, where R is the resistance and C is the capacitance. This relationship indicates how quickly the circuit charges or discharges.

In an RL circuit, the current during transient buildup is given by:

• I(t) = (V/R)(1 + e^(-Rt/L))

• I(t) = (V/R)(e^(Rt/L))

• I(t) = (V/R)(1 - e^(-Rt/L))

• I(t) = (V/R)(e^(-Rt/L))

Answer explanation

In an RL circuit, the transient current builds up according to the formula I(t) = (V/R)(1 - e^(-Rt/L)). This reflects the gradual increase of current over time, starting from zero and approaching V/R.

The time constant (τ) of an RL circuit is:

• τ = LR

• τ = R/L

• τ = L/R

• τ = L + R

Answer explanation

The time constant (τ) of an RL circuit is defined as τ = L/R, where L is the inductance and R is the resistance. This relationship shows how the circuit responds to changes in current over time.

The purpose of an inductor in a circuit is to:

• Oppose changes in current

• Oppose changes in voltage

• Store energy in an electric field

• Dissipate energy as heat

Answer explanation

An inductor opposes changes in current due to its property of inductance. When the current through an inductor changes, it generates a back electromotive force (EMF) that resists the change, making 'oppose changes in current' the correct choice.

In an RC circuit, the voltage across the resistor during discharging is:

• V_R(t) = V_0 * e^(-t/RC)

• V_R(t) = V_0 * sin(t/RC)

• V_R(t) = V_0 * e^(t/RC)

• V_R(t) = V_0 * (1 - e^(-t/RC))

Answer explanation

During discharging in an RC circuit, the voltage across the resistor decreases exponentially. The correct formula is V_R(t) = V_0 * e^(-t/RC), which shows this decay over time.

The energy stored in a capacitor is in the form of:

• Electrostatic potential energy

• Kinetic energy

• Thermal energy

• Magnetic energy

Answer explanation

The energy stored in a capacitor is in the form of electrostatic potential energy, which arises from the separation of charges within the capacitor. This distinguishes it from kinetic, thermal, or magnetic energy.

The voltage across an inductor leads the current by:

• 45 degrees

• 90 degrees

• 180 degrees

• 0 degrees

Answer explanation

In an inductor, the voltage leads the current by 90 degrees due to the nature of inductive reactance, which causes a phase shift. This means that when the current reaches its peak, the voltage is already at its maximum.

The reactance of an inductor (XL​) is given by:

• XL = ωL

• XL = L/ω

• XL = 1/ω

• XL = R

Answer explanation

The reactance of an inductor (XL) is defined by the formula XL = ωL, where ω is the angular frequency and L is the inductance. This relationship shows how the reactance increases with frequency.

The reactance of a capacitor (XC​) is given by:

• XC = 2πfC^2

• XC = 1 / (2πfC)

• XC = C / (2πf)

• XC = 2πfC

Answer explanation

The reactance of a capacitor (XC) is defined as XC = 1 / (2πfC). This formula shows that reactance is inversely proportional to both frequency (f) and capacitance (C), making this the correct choice.