On this page you will find few practice question in Physics (A.C Circuits) which will enhance your preparation for the forthcoming GCE Exam.

**TOPIC: A.C CIRCUITS**

Watch the video tutorial below, for detailed explanation of A.C Circuits, then answer the questions that follows, below the video.

## AC CIRCUITS EXPLAINED

*AC* stands for “Alternating Current,” meaning voltage or current that changes polarity or direction, respectively, over time.

Alternating Current Circuits or AC circuits are simply **circuits powered by an Alternating Source, either current or voltage**. An Alternating Voltage or Current is one in which the amount of either the voltage or the current alters about a distinct mean value and reverses direction periodically.

Components of *AC circuits* are resistors, capacitors, and inductors. All these passive electrical elements have one property in common; they regulate current.

The main components of AC circuits are resistors, capacitors, and inductors.

All these passive electrical elements have one property in common; they restrict electric current in a circuit coil but in completely different ways.

Figure above shows the plot of **alternating voltage** and **alternating current** as a function of time in a circuit that has only a resistor and a source of alternating current — an ac generator.

Because the voltage and current reach their maximum values at the same time, they are **in phase**. Ohm’s law and the previous expressions for power are valid for this circuit if the **root mean square** (rms) of the voltage and the rms of the current, sometimes called the **effective value**, are used. These relationships are

Ohm’s law is expressed thus: *V _{R} *=

*IR*, where

*V*is the rms voltage across the resistor and

_{R}*I*is the rms in the circuit.

**Passive Components in AC Circuits**

We can name *R* as resistance, *C* as capacitance, and *L* as inductance. Whether we use resistors in DC or AC circuits, they always have the same value of resistance in the system no matter what is the supply frequency. It is all because resistors are identified to be pure, having parasitic characteristics such as zero inductance L = 0 and infinite capacitance C = ∞. Also, for a fully resistive circuit, we always have an in-phase voltage and current, so we can find the power consumed at any instant by multiplying the voltage by the current.

On the other hand, capacitors and inductors have a distinct type of AC resistance known as *reactance, as mentioned before* (X_{L} and X_{C}). Reactance also blocks the current flow, but the value of reactance is not a fixed amount for one capacitor or inductor compared to a resistor with a fixed value of resistance. The reactance quantity for an inductor or a capacitor is based on the frequency of the supply current and the DC value of the element itself.

**Fully Resistive Circuit**

Resistors impede, regulate, or set the flow of current in a distinct path or impose a voltage cut in an electrical circuit base on this current flow. Resistors have a sort of impedance called *resistance* ( R ). The resistive quantity of a resistor is measured in Ohms, Ω, and can be found either in a fixed value or a shifting value (potentiometers).

Impedance and current value can be found using the following equations:

Z=*VR*/*IR* =*R*

**Fully Capacitive Circuit **

The capacitor is a component that has the capacity and can save energy in the shape of an electrical charge, the same as a small battery. The capacitance quantity of a capacitor is measured in Farads (F), and at the DC circuit, a capacitor has an infinite impedance (open-circuit). On the other hand, a capacitor has zero impedance (short-circuit) at very high frequencies. Impedance and current value can be found using the following equations:

XC = *VC*/*IC* = 1/2*πfC*

**Fully Inductive Circuit **

An inductor includes a coil of wire that induces a magnetic field within itself or a central core due to the current flowing through the coil. The inductance quantity of an inductor is measured in the Henries unit (H). At DC circuits, an inductor is a short-circuit and has zero impedance. In contrast, at high frequencies, an inductor has an infinite impedance (open-circuit). Impedance and current value can be found using the following equations:

*XL*=*VL*/*IL*=2*πfL*

**Series AC Circuits**

We can connect passive components together in series combinations in AC circuits to form RC, RL, and LC circuits, as explained below.

**Series RC Circuit**

The circuit and the equation for the series RC circuit are:

**Series RL Circuit**

The circuit diagram and the equation for the series RL circuit are:

**RLC Circuits**

We can connect all three passive components in an AC circuit, both series and parallel RLC combinations, as explained below.

**Series RLC Circuit**

The circuit diagram and the equation for the series RLC circuit are:

## PHYSICS: WAEC GCE PRACTICE QUESTIONS

**NOTE: TYPE YOUR ANSWERS INTO THE COMMENT BOX BELOW THESE QUESTIONS, THE CORRECTIONS WILL BE POSTED SOON.**

**1.** In a series R-L-C circuit, R = 10Ω, Xc= 4Ω and XL = 9Ω. The impedance of the circuit is

**A.**4.1Ω**B.**5.0Ω**C.**10.8Ω**D.**11.2Ω

**2.** In an ac circuit when the supply voltage frequency is equal to the resonant frequency, the current

**A.**leads the supply voltge by 90^{o}**B.**lags behind the supply voltage by 90^{o}**C.**leads the supply voltage by 45^{o}**D.**is in phase with the supply voltage

**3.** An a.c circuit of e.m.f 12V has a resistor of resistance 8Ω connected in series to an inductor of inductive reactance 16Ω and a capacitor capacitive reactance 10Ω. The current flow in the circuit is

A) 1.4A

B) 1.2A

C) 12.0A

D) 14.0A

**4.** When an alternating current given by I = 10sin (120π)t passes through a 12Ω resistor, the power dissipated in the resistor is

A) 1200W

B) 600W

C) 120W

D) 30W

**5.** A 15 μFμF capacitor is connected to a 240V, 50Hz ac. source. Calculate the reactance of the capacitance [π=3.142π=3.142]

**A.**16ΩΩ**B.**68ΩΩ**C.**106ΩΩ**D.**212Ω

**TYPE YOUR ANSWERS INTO THE COMMENT BOX BELOW, THE CORRECTIONS WILL BE POSTED SOON.**

## THEORY QUESTION

An RLC series circuit consists of a 100ΩΩ resistor, 0.05 H inductor and a 25 μμ capacitor. A 220 V, 50 Hz mains voltage is applied across the circuit. Calculate the:

(i) impedance;

(ii) current. (ππ = 3.14)

**TYPE YOUR ANSWERS INTO THE COMMENT BOX BELOW, THE CORRECTIONS WILL BE POSTED SOON.**