a 22 kilo ohm resistor having a tolerance of 10% has failed. you have on hand five resistors, valued at 120, 220, 47, 33 and 120 kilo ohm respectively. what combination of these would you choose to connect in parallel to replace the failed component?
Select:
R1 = 33k
R2 = 120k
R3 = 120k
1/Req = 1/33k + 1/120k + 1/120k = 0.0469697k
Req = 21.3k
How do i sketch the circuit diagram of the resultant?
To replace the 22 kilo ohm resistor with a tolerance of 10%, we need to find a combination of resistors that can give us a value close to 22 kilo ohms.
To calculate the equivalent resistance of resistors connected in parallel, we use the formula:
1/Req = 1/R1 + 1/R2 + 1/R3 + ...
Now let's calculate the equivalent resistance of each combination. We'll start with a combination of two resistors:
1/Req = 1/R1 + 1/R2
For R1 = 120 kilo ohms and R2 = 220 kilo ohms:
1/Req = 1/120 + 1/220
1/Req = 0.0083 + 0.0045
1/Req = 0.0128
Req = 1/0.0128
Req ≈ 78 kilo ohms
Next, let's try a combination of three resistors:
1/Req = 1/R1 + 1/R2 + 1/R3
For R1 = 120 kilo ohms, R2 = 220 kilo ohms, and R3 = 47 kilo ohms:
1/Req = 1/120 + 1/220 + 1/47
1/Req = 0.0083 + 0.0045 + 0.0213
1/Req = 0.0341
Req = 1/0.0341
Req ≈ 29.3 kilo ohms
Based on the calculations, neither of these combinations gives us an equivalent resistance close to 22 kilo ohms. Therefore, we'll need to try a different combination. Let's try a combination of four resistors:
1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4
For R1 = 120 kilo ohms, R2 = 220 kilo ohms, R3 = 47 kilo ohms, and R4 = 33 kilo ohms:
1/Req = 1/120 + 1/220 + 1/47 + 1/33
1/Req = 0.0083 + 0.0045 + 0.0213 + 0.0303
1/Req = 0.0644
Req = 1/0.0644
Req ≈ 15.5 kilo ohms
Great! The combination of these four resistors gives us an equivalent resistance of approximately 15.5 kilo ohms, which is close to the desired 22 kilo ohms. Therefore, to replace the failed 22 kilo ohm resistor, you can connect the resistors with values 120 kilo ohms, 220 kilo ohms, 47 kilo ohms, and 33 kilo ohms in parallel.
To determine the appropriate combination of resistors to replace the failed 22 kilo-ohm resistor, we need to calculate the preferred equivalent resistance using the available resistors. Here's how you can approach it:
1. Calculate the acceptable range for the failed resistor:
The 10% tolerance means that the failed resistor could have a resistance within a range of +/- 10% of its nominal value.
Therefore, the range for the failed 22 kilo-ohm resistor would be:
Minimum Resistance = 22 kilo-ohm - (22 kilo-ohm * 10%) = 19.8 kilo-ohm
Maximum Resistance = 22 kilo-ohm + (22 kilo-ohm * 10%) = 24.2 kilo-ohm
2. Check the available resistors:
The available resistors are: 120 kilo-ohm, 220 kilo-ohm, 47 kilo-ohm, 33 kilo-ohm, and 120 kilo-ohm.
3. Find the combination of resistors that forms an equivalent resistance within the acceptable range:
Combination 1: 120 kilo-ohm + 47 kilo-ohm = 167 kilo-ohm
Combination 2: 33 kilo-ohm + 47 kilo-ohm + 120 kilo-ohm = 200 kilo-ohm
Combination 3: 220 kilo-ohm + 47 kilo-ohm = 267 kilo-ohm
Combination 4: 220 kilo-ohm + 33 kilo-ohm + 47 kilo-ohm = 300 kilo-ohm
Combination 5: 220 kilo-ohm + 120 kilo-ohm = 340 kilo-ohm
4. Select the combination that falls within the range of the failed resistor:
Since the acceptable range for the failed 22 kilo-ohm resistor is 19.8 kilo-ohm to 24.2 kilo-ohm, the closest match is Combination 1 with an equivalent resistance of 167 kilo-ohm.
Therefore, to replace the failed 22 kilo-ohm resistor, you would connect a 120 kilo-ohm resistor in parallel with a 47 kilo-ohm resistor, resulting in an equivalent resistance of approximately 167 kilo-ohm.