Determine the total resistance of each of the following parallel circuits. (You can calculate the total resistance from the current and voltage using Ohm’s law, or use the Ohmmeter to measure the resistance directly.)
A. A parallel circuit with a 20-ohm resistor and a 10-ohm resistor. 6.7 ohm
B. A parallel circuit with two 20-ohm resistors and a 10-ohm resistor. 5 ohm
C. A parallel circuit with a 15-ohm light bulb and a 20-ohm resistor. _____
D. A parallel circuit with two 100-ohm resistors and a 20-ohm resistor.___
E. A parallel circuit with a 10-ohm, 20-ohm, 100-ohm and 200-ohm resistor. _____
I tried to complete A and B, but I got stuck on the rest. Can anyone help me out!?
D. 1/R = 2/100 +1/20 = 2/100 + 5/100 = 7/100
so R = 100/7 = 14.3 ohms
E. 1/R = 1/10 + 1/20 + 1/100 + 1/200
= 20/200 + 10/200 + 2/200 + 1/200 = 33/200
so R = 200/33 = 6.06 Ohms
Sure! Let me guide you through the process of calculating the total resistance for circuits C, D, and E.
C. A parallel circuit with a 15-ohm light bulb and a 20-ohm resistor:
To calculate the total resistance in a parallel circuit, you can use the formula:
1/RT = 1/R1 + 1/R2 + ...
In this case, you have two resistors in parallel: a 15-ohm light bulb and a 20-ohm resistor.
Let's substitute the values into the formula:
1/RT = 1/15 + 1/20
To simplify this calculation, you can find a common denominator for 15 and 20, which is 60:
1/RT = 4/60 + 3/60
Combining the fractions:
1/RT = 7/60
Now, let's find the reciprocal of both sides to isolate RT:
RT = 60/7
After evaluating the fraction, the total resistance is approximately 8.57 ohms.
D. A parallel circuit with two 100-ohm resistors and a 20-ohm resistor:
Again, we'll use the formula for parallel resistances:
1/RT = 1/R1 + 1/R2 + ...
In this case, you have three resistors: two 100-ohm resistors and a 20-ohm resistor.
Let's substitute the values into the formula:
1/RT = 1/100 + 1/100 + 1/20
Simplifying the calculation:
1/RT = 2/200 + 2/200 + 10/200
Combining the fractions:
1/RT = 14/200
Now, calculating the reciprocal to solve for RT:
RT = 200/14
After evaluating the fraction, the total resistance is approximately 14.29 ohms.
E. A parallel circuit with a 10-ohm, 20-ohm, 100-ohm, and 200-ohm resistor:
Once again, we'll use the formula for parallel resistances:
1/RT = 1/R1 + 1/R2 + ...
In this case, you have four resistors: 10 ohms, 20 ohms, 100 ohms, and 200 ohms.
Let's substitute the values into the formula:
1/RT = 1/10 + 1/20 + 1/100 + 1/200
Simplifying the calculation:
1/RT = 20/200 + 10/200 + 2/200 + 1/200
Combining the fractions:
1/RT = 33/200
Now, solving for RT:
RT = 200/33
After evaluating the fraction, the total resistance is approximately 6.06 ohms.
I hope this helps! Let me know if you have any further questions.
C. A parallel circuit with a 15-ohm light bulb and a 20-ohm resistor. _____
It does not matter if it is a light bulb. Its resistance is 15 ohms.
1/R = 1/15+ 1/20 = 20/300 + 15/300 = 35/300
so
R = 300/35 = 8.57 ohms