1. A parallel circuit contains four branches with resistors values of 4.7k, 5.6k

Question

1. A parallel circuit contains four branches with resistors values of 4.7k, 5.6k, 8.1k and 10k. Which branch has the largest current flow?



2. A 100? resistor is in parallel with a 220 ? resistor. The total resistance of the circuit is:
a. <100 ? b. 100 ? < and < 220 ? c. 220 ? < and < 320 ? d. > 320 ?


3. In the circuit below, what is the value for I3 if IT = 100mA, I1 = 40mA and I2 = 25mA?


The above circuit schematic consists of four vertical branches connected together in parallel in a circuit. The first branch on the left consists of a battery labeled V1 with its positive lead pointing upwards. The second branch consists of a resistor labeled R1. The third branch consists of a second resistor labeled R2, and the fourth branch consists of a third resistor labeled R3. The current flowing out of the positive end of the battery is denoted by an arrow labeled IT. The current flowing into R1 is denoted by an arrow labeled I1 drawn vertically alongside R1 pointing downwards. The current flowing into R2 is denoted by an arrow labeled I2 drawn vertically alongside R2 pointing downwards. The current flowing into R3 is denoted by an arrow labeled I3 drawn vertically alongside R3 pointing downwards. The negative lead of the battery is connected to ground.

4. In the circuit below, what is the current in each branch if the R4 resistor becomes open?

The above circuit schematic consists of five vertical branches connected together in parallel in a circuit. The first branch on the left consists of a battery labeled V1 with its positive lead pointing upwards. The second branch consists of a resistor labeled R1. The third branch consists of a second resistor labeled R2. The fourth branch consists of a third resistor labeled R3, and the fifth branch consists of a fourth resistor labeled R4. The current flowing into R1 is denoted by an arrow labeled 10 mA drawn vertically alongside R1 pointing downwards. The current flowing into R2 is denoted by an arrow labeled 10mA drawn vertically alongside R2 pointing downwards. The current flowing into R3 is denoted by an arrow labeled 10 mA drawn vertically alongside R3 pointing downwards. The current flowing into R4 is denoted by an arrow labeled 10 mA drawn vertically alongside R4 pointing downwards. The negative lead of the battery is connected to ground.


5. What is the equivalent resistance for the circuit shown below?

The above circuit schematic consists of three vertical branches connected together in parallel in a circuit. The first branch on the left consists of a battery labeled 15V with its positive lead pointing upwards. The second branch consists of a resistor labeled 4.7 kOhm. The third branch consists of a second resistor labeled 10kOhm. The negative lead of the battery is connected to ground.

6. In the circuit below, what is the current flow through resistor R2?

The above circuit schematic consists of four vertical branches connected together in parallel in a circuit. The first branch on the left consists of a battery labeled 12 V with its positive lead pointing upwards. The second branch consists of a resistor labeled R1 of value 220 Ohm. The third branch consists of a second resistor labeled R2 of value 330Ohm. The fourth branch consists of a third resistor labeled R3 of value 510 Ohm. The negative lead of the battery is connected to ground.
7. For the circuit below, each branch has equal resistance. What value of resistance (R) will produce an equivalent resistance of 33.3 ??

The above circuit schematic consists of two vertical branches connected together in parallel in a circuit. The first branch on the left consists of a battery labeled V1 with its positive lead pointing upwards. The second branch consists of a resistor labeled R1, and the third branch consists of a second resistor labeled R2. The negative lead of the battery is connected to ground. The value of R1 is equal to the value of R2 and equal to R.


8. For the circuit below, each branch has equal resistance. What value of resistance (R) will produce an equivalent resistance of 33.3 ??



The above circuit schematic consists of four vertical branches connected together in parallel in a circuit. The first branch on the left consists of a battery labeled V1 with its positive polarity pointing upwards. The second branch consists of a resistor labeled R1. The third branch consists of a second resistor labeled R2, and the fourth branch consists of a third resistor labeled R3. The negative lead of the battery is connected to ground.
The value of R1 is equal to the value of R2 and equal to the value of R3 and equal to R.

9. Which circuit has the highest current flow?

This question has two circuit schematics side by side. The first circuit schematic on the left consists of a 10 Volt battery drawn vertically with its positive polarity pointing upwards connected with two resistors in series. The first resistor connected to the positive lead of the battery is labeled 1 kOhm, and is drawn horizontally at the top of the circuit. The second resistor is labeled 6.8 kOhm, and is drawn horizontally at the bottom of the circuit. The negative lead of the battery is connected to ground.
The second circuit schematic shown on the right consists of three vertical branches connected together in parallel in a circuit. The first branch on the left consists of a battery labeled 10 V with its positive polarity pointing upwards. The second branch consists of a resistor labeled 1.0 kOhm. The third branch consists of a second resistor labeled 6.8 kOhm. The negative lead of the battery is connected to ground.



10. In Problem 9, what is the power dissipation for each circuit?

Explanation / Answer

In this case the largest current flow through 4.7k resistor
2) 100 in parallel with 220, the resultant resistance R = (100)(220)/(100+220) = 68.75 R < 100
3) Applying KCL IT = I1 + I2 + I3 100*10-3 = 40*10-3 + 25*10-3 + I3 I3 = 35mA
4) The total current IT = I1 + I2 + I3 + I4 IT = (10+10+10+10) m = 40mA Since the current throught each branch is same, their resistors will be equal to say R
If R4 is open, the circuit will have three resistors in parallel Now the current through each resistor will be = 40mA/3 = 13.33mA
5) The equivalent resistance as seen by the source is R = 4.7k parallel 10k R = (4700)(10000)/(4700+10000) R = 3.2k
6) The current through R2 will be I2 = V / R2 I2 = 12 / 330 I2 = 0.03636A = 36.36mA
7) Two equal resistances in parallel , the equivalent will be RT = (R)(R)/(R+R) = R/2 R = 2 RT R = (2)(33.3) R = 66.6
8) Three equal resistors in parallel, the equivalent resistance will be (1/RT ) = (1/R) + (1/R) + (1/R) 1/RT = 3/R R = 3RT = 3(33.3) R = 99.9
9) In the first circuit , the total resistance is RT = 1k + 6.8k = 7.8k Current drawn is I = V / RT = 10 / 7800 = 1.282mA
In the second circuit , the total resistance is RT = 1k || 6.8k = (1000)(6800)/(7800) = 872 Current drawn is I = V / RT = 10 / 872 = 0.0115A = 11.5mA Second circuit draws more current
10) Power dissipation in the first circuit P = IV = (1.282m)(10)=12.282mW Power dissipation in the second circuit P = IV = (11.5m)(10) = 115mW







100*10-3 = 40*10-3 + 25*10-3 + I3 I3 = 35mA
4) The total current IT = I1 + I2 + I3 + I4 IT = (10+10+10+10) m = 40mA Since the current throught each branch is same, their resistors will be equal to say R
If R4 is open, the circuit will have three resistors in parallel Now the current through each resistor will be = 40mA/3 = 13.33mA
5) The equivalent resistance as seen by the source is R = 4.7k parallel 10k R = (4700)(10000)/(4700+10000) R = 3.2k
6) The current through R2 will be I2 = V / R2 I2 = 12 / 330 I2 = 0.03636A = 36.36mA
7) Two equal resistances in parallel , the equivalent will be RT = (R)(R)/(R+R) = R/2 R = 2 RT R = (2)(33.3) R = 66.6
8) Three equal resistors in parallel, the equivalent resistance will be (1/RT ) = (1/R) + (1/R) + (1/R) 1/RT = 3/R R = 3RT = 3(33.3) R = 99.9
9) In the first circuit , the total resistance is RT = 1k + 6.8k = 7.8k Current drawn is I = V / RT = 10 / 7800 = 1.282mA
In the second circuit , the total resistance is RT = 1k || 6.8k = (1000)(6800)/(7800) = 872 Current drawn is I = V / RT = 10 / 872 = 0.0115A = 11.5mA Second circuit draws more current
10) Power dissipation in the first circuit P = IV = (1.282m)(10)=12.282mW Power dissipation in the second circuit P = IV = (11.5m)(10) = 115mW







I3 = 35mA
4) The total current IT = I1 + I2 + I3 + I4 IT = (10+10+10+10) m = 40mA Since the current throught each branch is same, their resistors will be equal to say R
If R4 is open, the circuit will have three resistors in parallel Now the current through each resistor will be = 40mA/3 = 13.33mA
5) The equivalent resistance as seen by the source is R = 4.7k parallel 10k R = (4700)(10000)/(4700+10000) R = 3.2k
6) The current through R2 will be I2 = V / R2 I2 = 12 / 330 I2 = 0.03636A = 36.36mA
7) Two equal resistances in parallel , the equivalent will be RT = (R)(R)/(R+R) = R/2 R = 2 RT R = (2)(33.3) R = 66.6
8) Three equal resistors in parallel, the equivalent resistance will be (1/RT ) = (1/R) + (1/R) + (1/R) 1/RT = 3/R R = 3RT = 3(33.3) R = 99.9
9) In the first circuit , the total resistance is RT = 1k + 6.8k = 7.8k Current drawn is I = V / RT = 10 / 7800 = 1.282mA
In the second circuit , the total resistance is RT = 1k || 6.8k = (1000)(6800)/(7800) = 872 Current drawn is I = V / RT = 10 / 872 = 0.0115A = 11.5mA Second circuit draws more current
10) Power dissipation in the first circuit P = IV = (1.282m)(10)=12.282mW Power dissipation in the second circuit P = IV = (11.5m)(10) = 115mW







IT = (10+10+10+10) m = 40mA Since the current throught each branch is same, their resistors will be equal to say R
If R4 is open, the circuit will have three resistors in parallel Now the current through each resistor will be = 40mA/3 = 13.33mA
5) The equivalent resistance as seen by the source is R = 4.7k parallel 10k R = (4700)(10000)/(4700+10000) R = 3.2k
6) The current through R2 will be I2 = V / R2 I2 = 12 / 330 I2 = 0.03636A = 36.36mA
7) Two equal resistances in parallel , the equivalent will be RT = (R)(R)/(R+R) = R/2 R = 2 RT R = (2)(33.3) R = 66.6
8) Three equal resistors in parallel, the equivalent resistance will be (1/RT ) = (1/R) + (1/R) + (1/R) 1/RT = 3/R R = 3RT = 3(33.3) R = 99.9
9) In the first circuit , the total resistance is RT = 1k + 6.8k = 7.8k Current drawn is I = V / RT = 10 / 7800 = 1.282mA
In the second circuit , the total resistance is RT = 1k || 6.8k = (1000)(6800)/(7800) = 872 Current drawn is I = V / RT = 10 / 872 = 0.0115A = 11.5mA Second circuit draws more current
10) Power dissipation in the first circuit P = IV = (1.282m)(10)=12.282mW Power dissipation in the second circuit P = IV = (11.5m)(10) = 115mW







I2 = 12 / 330 I2 = 0.03636A = 36.36mA
7) Two equal resistances in parallel , the equivalent will be RT = (R)(R)/(R+R) = R/2 R = 2 RT R = (2)(33.3) R = 66.6
8) Three equal resistors in parallel, the equivalent resistance will be (1/RT ) = (1/R) + (1/R) + (1/R) 1/RT = 3/R R = 3RT = 3(33.3) R = 99.9
9) In the first circuit , the total resistance is RT = 1k + 6.8k = 7.8k Current drawn is I = V / RT = 10 / 7800 = 1.282mA
In the second circuit , the total resistance is RT = 1k || 6.8k = (1000)(6800)/(7800) = 872 Current drawn is I = V / RT = 10 / 872 = 0.0115A = 11.5mA Second circuit draws more current
10) Power dissipation in the first circuit P = IV = (1.282m)(10)=12.282mW Power dissipation in the second circuit P = IV = (11.5m)(10) = 115mW







R = (2)(33.3) R = 66.6
8) Three equal resistors in parallel, the equivalent resistance will be (1/RT ) = (1/R) + (1/R) + (1/R) 1/RT = 3/R R = 3RT = 3(33.3) R = 99.9
9) In the first circuit , the total resistance is RT = 1k + 6.8k = 7.8k Current drawn is I = V / RT = 10 / 7800 = 1.282mA
In the second circuit , the total resistance is RT = 1k || 6.8k = (1000)(6800)/(7800) = 872 Current drawn is I = V / RT = 10 / 872 = 0.0115A = 11.5mA In the second circuit , the total resistance is RT = 1k || 6.8k = (1000)(6800)/(7800) = 872 Current drawn is I = V / RT = 10 / 872 = 0.0115A = 11.5mA Second circuit draws more current
10) Power dissipation in the first circuit P = IV = (1.282m)(10)=12.282mW Power dissipation in the second circuit P = IV = (11.5m)(10) = 115mW

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