Parallel Circuits
- 2. Parallel Circuit Theory Calculating Parallel Circuits Current Divider Rule Advantages/Disadvantages Applications Contents
- 3. Parallel Circuit A parallel circuit is a closed circuit in which the current divides into two or more paths before recombining to complete the circuit. Each load connected in a separate path receives the full circuit voltage, and the total circuit current is equal to the sum of the individual branch currents.
- 4. Theory Suppose, the values of three resistors are respectively R1, R2 and R3. One end of each resistor is connected at point A and the other ends of the resistors are connected at B so that same potential difference (VA – VB) exists between two ends of each resistor; here the potential of points A and B are respectively VA and VB. I A B
- 5. Here, current I after reaching at point A, gets divided into I1, I2 and I3 flowing through respective resistors R1, R2 and R3 reach at point B and after combining becomes the main current I. I= I1 + I2 + I3 …………………… (1) From the ohm’s law, we get 𝐼1 = 𝑉𝐴−𝑉𝐵 𝑅1 , 𝐼2 = 𝑉𝐴−𝑉𝐵 𝑅2 and 𝐼3 = 𝑉𝐴−𝑉𝐵 𝑅3 A B I I1 I2 I3 I
- 6. If the equivalent resistance of the circuit is R, then from ohm’s law 𝐼 = 𝑉𝐴−𝑉𝐵 𝑅𝑝 Now, inserting the values of I1, I2 and I3 in equation (1) 𝑉𝐴−𝑉𝐵 𝑅𝑝 = 𝑉𝐴−𝑉𝐵 𝑅1 + 𝑉𝐴−𝑉𝐵 𝑅2 + 𝑉𝐴−𝑉𝐵 𝑅3 1 𝑅𝑝 = 1 𝑅1 + 1 𝑅2 + 1 𝑅3 If the number of resistors is n 1 𝑅𝑝 = 1 𝑅1 + 1 𝑅2 + 1 𝑅3 +……………….+ 1 𝑅𝑛
- 7. Calculating Parallel Circuits Total Resistance To find the total resistance of a parallel circuit, we have to follow the law given below: 𝟏 𝑹 𝑻 = 𝟏 𝑹 𝟏 + 𝟏 𝑹 𝟐 + ⋯ + 𝟏 𝑹 𝒏 I 𝑰 𝟏 𝑰 𝟐 I
- 8. An example We know, 𝟏 𝑹 𝑻 = 𝟏 𝑹 𝟏 + 𝟏 𝑹 𝟐 ⇒ 𝟏 𝑹 𝑻 = 𝟏 𝟐𝟎 + 𝟏 𝟏𝟎 ∴ 𝑹 𝑻 = 𝟔. 𝟔𝟔𝟕Ω It should be noticed that 𝑹 𝑻 is smaller than 𝑹 𝟏, 𝑹 𝟐 individually.
- 9. Now, we can also determine the total current with Ohm’s law. If the current flowing through the circuit is 𝑰 𝑻, then from Ohm’s law, Current, 𝑰 𝑻 = 𝑽 𝑹 𝑻 ∴ 𝑰 𝑻 = 𝟏𝟎 𝟔.𝟔𝟔𝟕 = 𝟏. 𝟒𝟗𝟗𝑨 𝑹 𝑻 = 𝟔. 𝟔𝟔𝟕Ω
- 10. Total Conductance As we know conductance is the reciprocal of resistance, which is given by 𝑮 = 𝟏 𝑹 Then it is easy to find out the total conductance of a parallel circuit using the formula below, 𝑮 𝑻 = 𝑮 𝟏 + 𝑮 𝟐
- 11. Which leads to, ⇒ 𝑮 𝑻 = 𝟏 𝑹 𝟏 + 𝟏 𝑹 𝟐 = 𝟏 𝟐𝟎 + 𝟏 𝟏𝟎 ∴ 𝑮 𝑻 = 𝟎. 𝟏𝟓Ω It should be noticed that 𝑮 𝑻 is greater than 𝑮 𝟏, 𝑮 𝟐 individually
- 12. Current Divider Rule Current Divider Current divider is a simple linear circuit that produces an output current that is a fraction of its input current . Current division refers to the splitting of current between the branches of the divider. Current Divider Rule The portion of the total current in the circuit that flows through a branch in the circuit is proportional to the ratio of the resistance of the branch to the total resistance.
- 13. General Points For two parallel elements of equal value, the current will divide equally. For parallel elements with different values, the smaller the resistance, the greater the share of input current. For parallel elements of different values, the current will split with a ratio equal to the inverse of their resistor values
- 14. Current Division The current associated with one resistor R1 in parallel with one other resistor is: totalI RR R I 21 2 1 totalI RR R I 21 1 2
- 15. The current associated with one resistor R1 in parallel with two or more resistors is: in eq eq eq I RR R I RR RR RRR 1 1 32 32 32 andwhere
- 16. Why do we use CDR? The current divider rule states that the portion of the total current in the circuit that flows through a branch in the circuit is proportional to the ratio of the resistance of the branch to the total resistance. This rule allows for a shortcut in determining the branch current in a parallel circuit, which is simply to multiply the ratio of the resistances by the total current.
- 17. Advantages 1. Every unit that is connected in a parallel circuit gets equal amount of voltage. 2. It becomes easy to connect or disconnect a new element without affecting the working of other elements. 3. If any fault happened to the circuit, then also the current is able to pass through the circuit through different paths.
- 18. Disadvantages 1. Every unit that is connected in a parallel circuit gets equal amount of voltage. 2. It becomes easy to connect or disconnect a new element without affecting the working of other elements. 3. If any fault happened to the circuit, then also the current is able to pass through the circuit through different paths.
- 19. Applications 1. Most household electrical wiring, such as receptacle outlets and lightning system typically uses parallel circuits. 2. Design of many electrical components such as- different kind of computer hardware is also based on parallel circuit. 3. In lightning systems, such as in a house or on a Christmas tree, often consists of multiple number of lamps connected parallelly. 4. In car system, dc power supply works parallelly. 5. Parallel circuits are one of the main building blocks used in the infrastructure that supplies power to large populations.
- 20. 6. Power ring Circuit The power ring circuit is also a parallel circuit.
- 21. Thank You!