Question

parallel circuits ii worksheet
each leg of the parallel circuits gets
a full dosage of the voltage
1.
1a. what is the r - total?
1b. what is the current \i\?
1c. what is the current thru each leg?
2.
2a. what is the r - total?
2b. what is the current \i\?
2c. what is the current thru each leg?
3.
3a. what is the r - total?
3b. what is the current \i\?
3c. what is the current thru each leg?

Explanation:

1A.

Step1: Calculate total resistance for parallel resistors

For two parallel resistors \(R_1 = 20\Omega\) and \(R_2=30\Omega\), the formula for total resistance \(R_{total}\) in parallel is \(\frac{1}{R_{total}}=\frac{1}{R_1}+\frac{1}{R_2}\).
Substitute values: \(\frac{1}{R_{total}}=\frac{1}{20}+\frac{1}{30}=\frac{3 + 2}{60}=\frac{5}{60}=\frac{1}{12}\), so \(R_{total}=12\Omega\).

1B.

Step1: Use Ohm's law \(I=\frac{V}{R}\)

Given \(V = 60V\) and \(R_{total}=12\Omega\) from 1A.
\(I=\frac{V}{R_{total}}=\frac{60}{12}=5A\)

1C.

Step1: Use Ohm's law for each resistor

For \(R_1 = 20\Omega\), \(I_1=\frac{V}{R_1}=\frac{60}{20}=3A\)
For \(R_2 = 30\Omega\), \(I_2=\frac{V}{R_2}=\frac{60}{30}=2A\)

2A.

Step1: Calculate total resistance for parallel resistors

For \(R_1 = 15\Omega\) and \(R_2=30\Omega\), \(\frac{1}{R_{total}}=\frac{1}{15}+\frac{1}{30}=\frac{2+1}{30}=\frac{3}{30}=\frac{1}{10}\), so \(R_{total}=10\Omega\)

2B.

Step1: Use Ohm's law \(I=\frac{V}{R}\)

Given \(V = 90V\) and \(R_{total}=10\Omega\) from 2A.
\(I=\frac{V}{R_{total}}=\frac{90}{10}=9A\)

2C.

Step1: Use Ohm's law for each resistor

For \(R_1 = 15\Omega\), \(I_1=\frac{V}{R_1}=\frac{90}{15}=6A\)
For \(R_2 = 30\Omega\), \(I_2=\frac{V}{R_2}=\frac{90}{30}=3A\)

3A.

Step1: Calculate total resistance for parallel resistors

For \(R_1 = 10\Omega\), \(R_2=20\Omega\) and \(R_3 = 60\Omega\), \(\frac{1}{R_{total}}=\frac{1}{10}+\frac{1}{20}+\frac{1}{60}=\frac{6 + 3+1}{60}=\frac{10}{60}=\frac{1}{6}\), so \(R_{total}=6\Omega\)

3B.

Step1: Use Ohm's law \(I=\frac{V}{R}\)

Given \(V = 120V\) and \(R_{total}=6\Omega\) from 3A.
\(I=\frac{V}{R_{total}}=\frac{120}{6}=20A\)

3C.

Step1: Use Ohm's law for each resistor

For \(R_1 = 10\Omega\), \(I_1=\frac{V}{R_1}=\frac{120}{10}=12A\)
For \(R_2 = 20\Omega\), \(I_2=\frac{V}{R_2}=\frac{120}{20}=6A\)
For \(R_3 = 60\Omega\), \(I_3=\frac{V}{R_3}=\frac{120}{60}=2A\)

Answer:

1A. \(12\Omega\)
1B. \(5A\)
1C. \(I_1 = 3A\), \(I_2=2A\)
2A. \(10\Omega\)
2B. \(9A\)
2C. \(I_1 = 6A\), \(I_2=3A\)
3A. \(6\Omega\)
3B. \(20A\)
3C. \(I_1 = 12A\), \(I_2=6A\), \(I_3 = 2A\)