What do they mean when the say calculate the effectiveness resistance of the parallel resistors if one resistor is 4 ohm and the other is 6 ohm and are connected in parallel?

To calculate the effective resistance of two resistors connected in parallel, you can use the formula:

1/Req = 1/R1 + 1/R2

Where:
- Req is the effective resistance
- R1 is the resistance of the first resistor (4 ohms)
- R2 is the resistance of the second resistor (6 ohms)

Plugging in the values:

1/Req = 1/4 + 1/6
1/Req = 3/12 + 2/12
1/Req = 5/12

Now, to find Req, take the reciprocal of both sides:

Req = 12/5
Req = 2.4 ohms

Therefore, the effective resistance of the two resistors connected in parallel is 2.4 ohms.

Equivalent Resistance of Parallel Resistors:

When multiple resistors are connected in parallel, the equivalent resistance is given by the formula:

```
1/Req = 1/R1 + 1/R2 + ... + 1/Rn
```

where:

- Req is the equivalent resistance
- R1, R2, ..., Rn are the resistances of the parallel resistors

Effectiveness Resistance:

The effectiveness resistance of a parallel resistor network measures how effectively the resistors work together to reduce the overall resistance compared to if they were connected in series. It is defined as:

```
Effectiveness Resistance = Req / N
```

where:

- Req is the equivalent resistance
- N is the number of resistors in parallel

Calculating the Effectiveness Resistance:

Given two resistors connected in parallel:

- R1 = 4 ohms
- R2 = 6 ohms

Step 1: Calculate the Equivalent Resistance:

```
1/Req = 1/R1 + 1/R2
1/Req = 1/4 + 1/6
1/Req = 5/12
Req = 12/5 = 2.4 ohms
```

Step 2: Calculate the Number of Resistors:

```
N = 2
```

Step 3: Calculate the Effectiveness Resistance:

```
Effectiveness Resistance = Req / N
Effectiveness Resistance = 2.4 / 2 = 1.2 ohms
```

Therefore, the effectiveness resistance of the parallel resistor network is 1.2 ohms, which means that the resistors are effectively reducing the overall resistance compared to if they were connected in series.

m’slawstatesthat
a.currentequalsvoltagetimesresistance
b.voltageequalscurrenttimesresistance
c.resistanceequalscurrentdividedbyvoltage
d.voltageequalscurrentsquaredtimesresistance
10.When the voltage across a resistor is doubled, the current will
e.triple
f.halve
g.double
h.notchange
11.A22Ωhalf-wattresistoranda220Ωhalf-wattresistorareconnectedacross
a10Vsource.Which one(s) will overheat?
a.22Ω
b.220 Ω
c.both
d.Neither
12.When10Vareappliedacrossa20Ωresistor,the
currentisa.10Ab. 0.5Ac. 200Ad. 2A
13.Whenthereare10mAofcurrentthrougha1.0KΩresistor,thevoltage
acrosstheresistoris
a. 100Vb. 0.1Vc. 10kVd. 10V
14.If 20 V are applied across a resistor and there are 6.06 mA of current, the resistance is
a. 3.3 KΩb. 33KΩc. 330Ωd. 3.03 KΩ
15.Acurrentof250 µAthrough a4.7kΩresistor producesavoltagedrop of
a.53.2b. 1.175 mVc. 18.8Vd 1.175V
16.Fiveequal-valueresistorsareconnectedinseriesandthereisacurrentof2mAinto
thefirstresistor.Theamountofcurrent outofthesecond resistoris
a.2 mAb. mAc. 4 mAd. 0.4 mA
17.Tomeasurethecurrentoutofthethirdresistorinacircuitconsistingoffourseries
resistors,an ammeter canbeplaced
a.betweenthethirdandfourthresistors
b.betweenthesecondand thirdresistors
c.atthepositiveterminalofthesource
d.at anypoint in thecircuit
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