Parallel circuits
Parallel circuits
Embedded Files
Parallel circuits have 1+ loops, each with often 1 components. As each components has 1 loop and one breaks, but the whole circuit is fine.
E.g. If a house's light bulb breaks, the other ones are fine.
Rules
Rules
A parallel circuit's total resistance is always lower than individual resistors and branches.
All components get their full potential difference.
Voltage per branch is the same as applied voltage.
Current divides across branches, with Ohm’s law to find its value.
IT is found with Ohm’s law and equal's all
branches' sum
For the circuit shown, current on R1 + current on R2 + current on R3 equals the IT: IR1 + IR2 + IR3
Current decreases if a component is burnt.
Grounding
Grounding
Most shocks (~95%) are from live to ground.
A transformer's secondary in a circuit isn't grounded. No voltage to ground.
You can touch line 1, line 2 or the neutral while grounded and not get a shock.
The ungrounded system's issue is that it will get a ground.
In graphic, L1 has a ground fault. This could be a faulty appliance or a damaged cable. Now L2 has 240 volts to ground, which can cause a serious shock.
Voltages:
L1 to L2 → 240 V
L1 to N → 120 V
L2 to N → 120 V
Bond wire on heater to N → 0 V
or
Total resistance
Total resistance
Resistances aren't added directly in parallel circuits.
Instead it's calculated in 2 ways.
Add the reciprocal values then take the reciprocal of that: E.g. 1/(1/R1 + 1/R2 + 1/R3)
Or add resistances divided by multiplied resistance: (R1 x R2)/(R1+R2), represented by 2 vertical bars "||": E.g. R1 || R2 || R3:
First execute "R1||R2": (R1 x R2)/(R1+R2)
= (R1 x R2)/(R1+R2) || R3.
Then {[(R1 x R2)/(R1+R2)] x R3}/{[(R1 x R2)/(R1+R2)] + R3}
On calculator
On calculator
To find RT for 3 resistors in parallel with a calculator, use the 𝑥−1 button for 1/x and the EXP button for × 10𝑥
Always enter all the numbers in the base unit into your calculator, don't convert 1.2 kΩ to 1,200 Ω or 2 MΩ to 2,000,000 Ω--Calculator does this.
A fx-991ms calculator does this by 2 ways:
Method 1
Enter 1.2 kΩ as 1.2 EXP 3. Kilo means 103.
EXP 3 means × 103 so if you enter 1.2 EXP 3, it's like entering 1.2 × 103.
Enter 2 MΩ as 2 EXP 6. Mega means 106. EXP 6 means × 106 so if you enter 2 EXP 6, it's like entering 1.2 × 106.
Method 2
fx-991ms has engineering prefixes: The button 6 has an small k (kilo) and above 7 has an small M (mega).
To turn on kilo prefix, enter shift 6.
To enter Mega prefix, enter shift 7.
Enter 1.2 kΩ as 1.2 {shift 6}. Do not enter the brackets. The display should show a 'k' after 1.2.
Enter 2 MΩ as 2{shift 7}. Don't include brackets. It should show an 'M' after the 2.
Method 1 works in any scientific calculator.
The fx-991ms calculator is a rare one with the engineering prefix function.
Find the 3 parallel resistors' RT:
1.2 EXP 3 𝑥−1 + 820 𝑥−1 + 2 EXP 6 𝑥−1 = denominator answer
Denominator answer 𝑥−1 = 487 = RT
Some to do it in a step
(1.2 EXP 3 𝑥−1 + 820 𝑥−1 + 2 EXP 6 𝑥−1) 𝑥 − 1 = 487
Example 1
Example 1
Calculate:
Total resistance
Current
VDROP per load
Power dissipated per load
RT = 100||200||300 = 1/((1/100) + (1/200) + (1/300)) = 54.55
Vdrop per load: 60V
Answer: As V = IR, we know voltage is the same on each branch, current is:
on each load:
IR1 = V/R1 = 60/100 = 0.6
IR2 = V/R2 = 60/200 = 0.3
IR3 = V/R3 = 60/300 = 0.2
IT = IR1 + IR2 + IR3 = 0.6 + 0.3 + 0.2 = 1.1 mA
Power dissipated per load: P = V²/R
PR1 = 60²/100 = 36 W
PR2 = 60²/200 = 18 W
PR3 = 60²/300 = 12 W
Example 2
Example 2
Calculate:
Current
Vdrop per load
Power dissipated per load
Vdrop per load: 120V
Current per load:
IR1 = V/R1 = 120/100 = 1.2
IR2 = V/R2 = 120/200 = 1.2
IR3 = V/R3 = 120/300 = 1.2
IT = IR1 + IR2 + IR3 = 1.2 x 3 = 3.6 mA
RT = 1/((1/100)x3) = 33.33 Ω
PT = (4² / 33.33)x3 = 432.04 W
RT = 1/((1/1000) + (1/1200) + (1/1300) + (1/980)) = 276.02 Ω
IR1 = 48/1000 = 0.048 A
IR2 = 48/1200 = 0.04 A
IR3 = 48/1300 = 0.037 A
IR4 = 48/980 = 0.049 A
IT = 0.174 A
Example 3
Example 3
Find:
RT
IT
Current per load
Current
Current
Example
Example
[3] Since voltage is the same per resistor here (9 V), use Ohm's law V/R:
Currents path in a parallel circuit.
As IT exits the positive battery terminal at point 1 and
splits off at point 2 to go R1,
some splits off at point 3 to go R2,
and the rest at point 4 goes to R3.
and returns to the battery through the battery's negative terminal.
All currents together = total current
Current divider law
Current divider law
(Kirchhoff's laws of) Current divider law says each resistance's RT ratio is the same ratio as an individual (branch) current to IT.
only used in parallel circuits, not in series circuits, as current is constant in all load and voltage is what's divided among components (by resistance).
Ix = current
Rx = resistance
AC and DC measurements
AC and DC measurements
Meter setting:
Resistance across an open component measures infinity (OL)--no continuity.
Resistance (Ω) – parallel
Voltage (V) – parallel
Current (A) - series
Opened DC circuits
Opened DC circuits
If a parallel circuit opens:
The whole potential voltage is seen across the open.
Resistors opened measures 0 V across each.
No continuity, no full path, no current flows.
Circuit current and power is 0.
Resistance across the open component is infinite.
Total circuit resistance is infinite.
Shorts in AC and DC circuits
Shorts in AC and DC circuits
If a parallel circuit has a short:
Creates a short across the power supply.
very dangerous
Resistance drops to zero.
Current rises til it trips the protection device.
Bathroom light
Bathroom light
A bathroom light has 4 identical light bulbs.
If all light bulb draws 1A if 120V is applied to it and the switch is closed, all light bulbs' voltages are 120 V.
If light bulb 1 burns open, IT, supplied by source, is lower (3A), then by Ohm’s law (𝑅 = 𝐸/𝐼), RT rises.
If each light bulb draws 1 A, IT through the closed swich is 4 A.
If a light bulb 1 burns open,
light bulb 1 won't light and won't draw current.
light bulb 2 to 4 will continue to draw 1A each.
current through the switch is now be 3A.
light bulb 2 to 4's brightness won't change.
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