Electric circuits – problems and solutions

1. R_{1}, = 6 Ω, R_{2} = R_{3} = 2 Ω, and voltage = 14 volt, determine the electric current in circuit as shown in figure below.

__Known :__

Resistor 1 (R_{1}) = 6 Ω

Resistor 2 (R_{2}) = 2 Ω

Resistor 3 (R_{3}) = 2 Ω

Voltage (V) = 14 Volt

__Wanted :__ Electric current (I)

__Solution :__

**Equivalent resistor (R) :**

R_{2} and R_{3} are connected in parallel. The equivalent resistor :

1/R_{23} = 1/R_{2} + 1/R_{3} = 1/2 + 1/2 = 2/2

R_{23 }= 2/2 = 1 Ω

R_{1 }and R_{23} are connected in series. The equivalent resistor :

R = R_{1} + R_{23} = 6 Ω + 1 Ω

R = 7 Ω ** **

Electric current (I) :

I = V / R = 14 / 7 = 2 Ampere

2. Which one of the electric circuits as shown below has the bigger current.

Solution :

The resistance of the resistor is R and the electric voltage is V.

__Answer A.__

R_{1}, R_{2} and R_{3} are connected in series. The equivalent resistor :

R_{A} = R_{1 }+ R_{2} + R_{3} = R + R + R = 3R

Electric current (I) :

__Answer B.__

R_{1}, R_{2} and R_{3} are connected in parallel. The equivalent resistor :

1/R = 1/R_{1 }+ 1/R_{2} + 1/R_{3} = 1/R + 1/R + 1/R = 3/R

R_{B} = R/3

Electric current (I) :

__Answer C.__

R_{2} and R_{3} are connected in parallel. The equivalent resistor :

1/R_{23} = 1/R_{2} + 1/R_{3} = 1/R + 1/R = 2/R

R_{23} = R/2

R_{1} and R_{23} are connected in series. The equivalent resistor :

R_{C} = R_{1} + R_{23} = R + R/2 = 2R/2 + R/2 = 3R/2

Electric current (I) :

__Answer D.__

R_{1 }and R_{2} are connected in parallel. The equivalent resistor :

1/R_{12 }= 1/R_{1 }+ 1/R_{2} = 1/R + 1/R = 2/R

R_{12 }= R/2

R_{12} and R_{3 }are connected in series. The equivalent resistor :

R_{D} = R_{12} + R_{3 }= R/2 + R = R/2 + 2R/2 = 3R/2

Electric current (I) :

3. R_{1} = 4 ohm, R_{2} = 6 ohm, R_{3} = 2 ohm, and V = 24 volt. What is the electric current in circuit as shown in figure below.

__Known :__

Resistor 1 (R_{1}) = 4 Ohm

Resistor 2 (R_{2}) = 6 Ohm

Resistor 3 (R_{3}) = 2 Ohm

Voltage (V) = 24 Volt

__Wanted :__ Electric current in circuit

__Solution :__

R_{1}, R_{2 }and R_{3 }are connected in series. The equivalent resistor :

R = R_{1} + R_{2} + R_{3 }= 4 + 6 + 2

R = 12 Ohm

Electric current :

I = V / R = 24 / 12 = 2 Ampere

4. Which one of the electric circuits as shown below has the bigger current.

Solution

**Electric current in circuit A.**

__The equivalent resistor :__

R_{1 }= 3 Ω, R_{2} = 4 Ω, R_{3} = 4 Ω, V = 12 Volt

R_{2} and R_{3} are connected in parallel. The equivalent resistor :

1/R_{23} = 1/R_{2} + 1/R_{3 }= 1/4 + 1/4 = 2/4 = 1/2

R_{23 }= 2/1 = 2 Ω

R_{1} and R_{23} are connected in series. The equivalent resistor :

R = R_{1} + R_{23 }= 3 Ω + 2 Ω = 5 Ω ** **

__Electric current (I) :__

I = V / R = 12 / 5 = 2.4 Ampere

**Electric current in circuit B.**

__The equivalent resistor :__

R_{1 }= 8 Ω, R_{2} = 2 Ω, R_{3} = 2 Ω, V = 36 Volt

R_{1}, R_{2} and R_{3} are connected in series. The equivalent resistor :

R = R_{1} + R_{2} + R_{3} = 8 + 2 + 2 = 12 Ω

__Electric current (I) :__

I = V / R = 36 / 12 = 3 Ampere

**Electric current in circuit C.**

__The equivalent resistor :__

R_{1 }= 4 Ω, R_{2} = 4 Ω, R_{3} = 6 Ω, V = 12 Volt

R_{2} and R_{3} are connected in parallel. The equivalent resistor :

1/R_{23} = 1/R_{2} + 1/R_{3 }= 1/4 + 1/4 + 1/6 = 3/12 + 3/12 + 2/12 = 8/12

R_{23 }= 12/8 = 1.5 Ω

__Electric current (I) :__

I = V / R = 12 / 1.5 = 8 Ampere

**Electric current in circuit D.**

__The equivalent resistor :__

R_{1 }= 3 Ω, R_{2} = 3 Ω, R_{3} = 3 Ω, R_{4} = 3 Ω, R_{5} = 6 Ω, V = 24 Volt

R_{2}, R_{3} and R_{4} are connected in parallel. The equivalent resistor :

1/R_{234} = 1/R_{2} + 1/R_{3 }+ 1/R_{4 }= 1/3 + 1/3 + 1/3 = 3/3

R_{234 }= 3/3 = 1 Ω

R_{1}, R_{234 }and R_{5} are connected in series The equivalent resistor :

R = R_{1} + R_{234 }+ R_{5 }= 3 + 1 + 6 = 9 Ω

__Electric current (I) :__

I = V / R = 24 / 9 = 2.6 Ampere

5. According to figure as shown below, determine :

A. Total resistance

B. Electric current in circuit

C. Current I_{1}

D. Current I_{2}

__Known :__

Resistor 1 (R_{1}) = 4 Ω

Resistor 2 (R_{2}) = 4 Ω

Resistor 3 (R_{3}) = 2 Ω

Resistor 4 (R_{4}) = 3 Ω

Electric voltage (V) = 12 Volt

__Solution :__

A. Total resistance (R)

Resistor R_{2} and resistor R_{3} are connected in series. The equivalent resistor :

R_{23} = R_{2} + R_{3} = 4 Ω + 2 Ω = 6 Ω

Resistor R_{23} and resistor R_{4 }are connected in parallel. The equivalent resistor :

1/R_{234} = 1/R_{23 }+ 1/R_{4} = 1/6 + 1/3 = 1/6 + 2/6 = 3/6

R_{234} = 6/3 = 2 Ω

Resistor R_{1} and resistor R_{234} are connected series. The equivalent resistor :

R = R_{1 }+ R_{234} = 4 Ω + 2 Ω = 6 Ω

The total resistance is 6 Ohm.

B. Electric current in circuit (I)

V = I R

*V = electric voltage, I = electric current, R = electric resistance*

Electric current :

I = V / R = 12 Volt / 6 Ohm = 2 Ampere

C. Electric current I_{1}

Electric current in resistor R_{1} = electric current in circuit = 2 Ampere.

D. Current I_{2}

Resistor R_{23} and resistor R_{4} are connected in parallel. The equivalent resistor R_{234} = 2 Ohm.

Electric current in resistor R_{234} = electric current in resistor R_{1} = 2 Ampere.

Voltage in resistor R_{234 } is:

V = I R_{234} = (2 A)(2 Ohm) = 4 Volt

Voltage in resistor R_{234 }= voltage in resistor R_{4} = voltage in resistor R_{23} = 4 Volt.

The equivalent resistor R_{23 }is 6 Ohm.

Electric current in resistor R_{23 }is :

I = V / R = 4 Volt / 6 Ohm = 2/3 Ampere

Electric current in resistor R_{23 }= Electric current in resistor R_{2} = electric current in resistor R_{3 }= 2/3 Ampere.

6. R_{1} = R_{2} = 10 Ω and R_{3} = R_{4} = 8 Ω. What is the electric current in circuit as shown in figure below ?

__Known :__

Resistor R_{1 }= Resistor R_{2} = 10 Ω

Resistor R_{3} = Resistor R_{4 }= 8 Ω

Electric voltage (V) = 12 Volt

__Wanted :__ electric current (I)

__Solution :__

__The ____equivalent resistor__

Resistor R_{3} and resistor R_{4 }are connected in parallel, the equivalent resistor :

1/R_{34} = 1/R_{3} + 1/R_{4} = 1/8 + 1/8 = 2/8

R_{34} = 8/2 = 4 Ω

Resistor R_{1}, R_{2 } and R_{34 }are connected in series, the equivalent resistor :

R = R_{1 }+ R_{2 }+ R_{34} = 10 Ω + 10 Ω + 4 Ω = 24 Ω

__Electric current :__

I = V / R = 12 Volt / 24 Ohm = 0,5 Volt/Ohm = 0.5 Ampere

7. If the internal resistance of battery ignored, what is the electric current in the circuit shown in figure below.

__Known :__

Resistor R_{1} = 3 Ohm

Resistor R_{2 }= 3 Ohm

Resistor R_{3} = 6 Ohm

Electric voltage (V) = 6 Volt

__Wanted :__ Electric current (I)

__Solution :__

__Equivalent resistor__

Resistor R_{1} and R_{2} are connected in series. The equivalent resistor :

R_{12 }= R_{1} + R_{2 }= 3 Ohm + 3 Ohm = 6 Ohm

Resistor R_{12} and resistor 3 are connected in parallel. The equivalent resistor :

1/R = 1/R_{12} + 1/R_{3 }= 1/6 + 1/6 = 2/6

R = 6/2 = 3 Ohm

Electric current :

I = V / R = 6 / 3 = 2 Ampere

8. What is the total electric current in circuit as shown in figure below.

__Known :__

Resistor R_{1} = 6 Ohm

Resistor R_{2} = 4 Ohm

Electric current (V) = 6 Volt

Internal resistance (r) = 0.6 Ohm

__Wanted :__ Electric current

__Solution :__

Resistor R_{1} and resistor R_{2} are connected in parallel. The equivalent resistor :

1/R_{P }= 1/R_{1} + 1/R_{2} = 1/6 + 1/4 = 4/24 + 6/24 = 10/24

R_{P} = 24/10 = 2.4 Ohm

Resistor R_{P} and internal resistance (r) are connected in series. The equivalent resistor :

R = R_{P} + r = 2.4 Ohm + 0.6 Ohm = 3.0 Ohm

Electric current in circuit :

I = V / R = 6 Volt / 3 Ohm = 2 Ampere

**What is an electric circuit?****Answer**: An electric circuit is a closed path or loop in which electric current can flow continuously. It typically consists of sources of voltage (like batteries), loads (like resistors, LEDs, motors), and conductors to connect them.

**What distinguishes a series circuit from a parallel circuit?****Answer**: In a series circuit, components are connected end-to-end, so there’s a single path for current. In a parallel circuit, components are connected across common points or junctions, providing multiple paths for current.

**How does Ohm’s Law relate voltage, current, and resistance in a circuit?****Answer**: Ohm’s Law states that the current ($I$) flowing through a conductor between two points is directly proportional to the voltage ($V$) across the two points and inversely proportional to the resistance ($R$). It’s represented as $I=V/R $.

**What is the role of a switch in an electric circuit?****Answer**: A switch controls the flow of current in a circuit. When closed, it allows current to flow; when open, it interrupts or stops the current flow.

**Why is a short circuit considered dangerous?****Answer**: In a short circuit, the resistance is very low, causing a very high current to flow. This can lead to overheating, fires, or damage to components and should be protected against with fuses or circuit breakers.

**What is the function of a fuse or a circuit breaker in a circuit?****Answer**: Both fuses and circuit breakers are protective devices designed to interrupt a circuit if the current exceeds a predetermined safe level. While fuses “blow” or “melt”, breaking the circuit, circuit breakers “trip”, and can be reset after they interrupt the circuit.

**How does Kirchhoff’s Current Law (KCL) describe currents at a junction in a circuit?****Answer**: Kirchhoff’s Current Law states that the sum of currents entering a junction is equal to the sum of currents leaving that junction. This is essentially a statement of the conservation of electric charge.

**What is the difference between AC (Alternating Current) and DC (Direct Current)?****Answer**: DC refers to the unidirectional flow of electric charge, typically from a battery or a DC power supply. AC, on the other hand, is an electric charge that changes direction periodically, like what’s supplied from the power grid in many countries.

**What does the term “ground” refer to in electrical circuits?****Answer**: “Ground” refers to a reference point in an electrical circuit from which other voltages are measured, or a common return path for electric current, or a direct physical connection to the Earth.

**Why are capacitors used in electric circuits?**

**Answer**: Capacitors store and release electrical energy. They’re used in circuits for various purposes, such as filtering, smoothing voltage fluctuations, coupling and decoupling AC signals, and timing elements in oscillators.