Question 1

Three 4.00-Ω resistors are connected in parallel to a 10.4-V battery.What is the current in any one of the resistors?

Accepted Answer

First, we need to calculate the total resistance of the circuit, which can be found using the formula:

1/R_total = 1/R1 + 1/R2 + 1/R3

Where R1, R2, and R3 are the resistances of the three resistors connected in parallel.

1/R_total = 1/4.00 Ω + 1/4.00 Ω + 1/4.00 Ω

1/R_total = 0.75 Ω

R_total = 1/0.75 Ω

R_total = 1.33 Ω

Next, we can use Ohm's Law to find the current in any one of the resistors:

I = V/R

I = 10.4 V / 4.00 Ω

I = 2.60 A

Therefore, the answer is C) 2.60 A.

Question 2

Resistors of values 7 Ω,15 Ω,and 25 Ω are connected in parallel across a fresh battery.Which resistor dissipates the greatest power?

Accepted Answer

In a parallel circuit, the voltage across each resistor is the same. Power dissipation in a resistor is given by $P = \frac{V^2}{R}$. With the same voltage across each, the resistor with the lowest resistance (7 Ω) dissipates the most power.

Question 3

Resistors of values 10 Ω,14 Ω,and 23 Ω are connected in series across a battery with a small internal resistance.Which resistor dissipates the greatest power?

Accepted Answer

When resistors are connected in series, the current through each resistor is the same. Therefore, the power dissipated by each resistor is given by P=I²R, where I is the current and R is the resistance of the resistor. Since power is proportional to resistance squared, the resistor with the highest resistance (23 Ω) will dissipate the most power.

Question 4

Three 6.0-Ω resistors are connected in parallel.What is their equivalent resistance?

Accepted Answer

The equivalent resistance, $R_{eq}$, of resistors in parallel is given by $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$. For three 6.0-Ω resistors in parallel, $\frac{1}{R_{eq}} = \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{1}{2}$, so $R_{eq} = 2.0$ Ω.

Question 5

If R₁ < R₂ < R₃,and if these resistors are connected in series in a circuit,which one dissipates the greatest power?

Accepted Answer

In a series circuit, the resistors with higher resistance will dissipate more power. As R₃ has the highest resistance among the given options, it will dissipate the greatest power. The power dissipated in a resistor can be calculated using the formula P=I^2R, where I is the current flowing through the resistor and R is its resistance. As the current flowing through all the resistors in a series circuit is the same, the resistor with the highest resistance will dissipate the most power.

Question 6

Resistors of values R₁ = 6.00 Ω,R₂ = 4.00 Ω,R₃ = 10.0 Ω,and R₄ = 7.00 Ω are combined as shown.What is the equivalent resistance for this combination?

Accepted Answer

To find the equivalent resistance, we need to first simplify the circuit by combining resistors in series and parallel.

Starting from the left, we can combine R1 (6.00 Ω) and R2 (4.00 Ω) in series to get a total resistance of 10.00 Ω.

Next, we can combine this result in parallel with R3 (10.0 Ω) using the formula:

1/Req = 1/10.00 Ω + 1/10.0 Ω

Solving for Req gives us:

Req = 5.71 Ω

Finally, we can combine this result in series with R4 (7.00 Ω) to get the total equivalent resistance:

Req = 5.71 Ω + 7.00 Ω = 12.71 Ω

Rounding to three significant figures, we get:

Req ≈ 10.7 Ω

Therefore, the answer is C.

Question 7

Two resistors of values 6.0 and 14.0 Ω are connected in parallel.This combination in turn is hooked in series with a 2.0-Ω resistor.What is the overall resistance of this combination?

Accepted Answer

The formula for calculating the total resistance of resistors connected in parallel is:

1/Rt = 1/R1 + 1/R2 + ...

where R1, R2, etc. are the values of each individual resistor.

Using this formula, we can find the equivalent resistance of the 6Ω and 14Ω resistors in parallel:

1/Rp = 1/6Ω + 1/14Ω
1/Rp = 0.1667 + 0.0714
1/Rp = 0.2381
Rp = 4.2 Ω

Now that we have the equivalent resistance of the parallel combination, we can use the formula for resistors in series to find the total resistance:

Rt = Rp + R3
Rt = 4.2Ω + 2.0Ω
Rt = 6.2 Ω

Therefore, the overall resistance of this combination is 6.2 Ω, which corresponds to choice C.

Question 8

If R₁ < R₂ < R₃,and if these resistors are connected in parallel in a circuit,which one has the highest current?

Accepted Answer

In parallel circuits, the resistor with the lowest resistance value has the highest current. R₁ has the lowest resistance value among the options, hence it will have the highest current.

Question 9

To find the equivalent resistance of the combination of resistors shown across the 28-V battery by the method of possibly repeated applications of combining resistors in series and /or combining resistors in parallel,the first step would be which of the following?

Accepted Answer

The first step would be to combine, in series, the two 3-Ω resistors and the 4-Ω resistor in the right-hand branch of the circuit since they are connected in series. This combination would result in a total resistance of 3 Ω + 3 Ω + 4 Ω = 10 Ω. Then, we can combine this 10 Ω resistor with the 5 Ω resistor in the middle of the circuit in parallel since they share a common node. This combination would result in a total resistance of 5 Ω x 10 Ω / (5 Ω + 10 Ω) = 3.33 Ω. Finally, we can combine the remaining three 3 Ω resistors and the 2 Ω resistor in series to get a total resistance of 3 Ω + 3 Ω + 3 Ω + 2 Ω = 11 Ω. Therefore, the equivalent resistance of the combination of resistors shown across the 28-V battery is 3.33 Ω + 11 Ω = 14.33 Ω.

Question 10

Three resistors with values R₁,R₂ and R₃,respectively,are connected in parallel.Which of the following expresses the total resistance,R_T,of the three resistors when connected in parallel?

Accepted Answer

The total resistance for resistors in parallel is given by the reciprocal of the sum of the reciprocals of each resistor's resistance.

Question 11

Three resistors,each with resistance R₁,are in parallel in a circuit.They are replaced by one equivalent resistor,R.Compare this resistor to the first resistor of the initial circuit.Which of the following statements is true?

Accepted Answer

When resistors are in parallel, they share the same voltage across them. Therefore, the voltage across the equivalent resistor $R$ is the same as the voltage across each individual resistor $R_{S}$.

Question 12

Three resistors,each of different value,are used in a circuit with a power source supplying 12 volts.For which of the following resistor combinations is the total power supplied the greatest?

Accepted Answer

When resistors are in parallel, the total resistance is reduced, and more current flows through the circuit. This means that more power is being supplied to the circuit. Therefore, with all three resistors in parallel, the total power supplied is the greatest.

Question 13

To find the equivalent resistance of the combination of resistors shown below by the method of possibly repeated applications of combining resistors in series and /or combining resistors in parallel,the first step would be which of the following?

Accepted Answer

The answer of To find the equivalent resistance of the...

Question 14

Five resistors each have resistance R.Three of the resistors are connected in series and this combination is then connected in parallel with the two other resistors which have been connected in series with each other.What is the equivalent resistance for this arrangement?

Accepted Answer

When three resistors are connected in series, their equivalent resistance is simply the sum of their individual resistances. Therefore, the three resistors in series have an equivalent resistance of 3R.

When two resistors are connected in series, their equivalent resistance is the sum of their individual resistances. Therefore, the two resistors in series have an equivalent resistance of 2R.

The final step is to find the equivalent resistance of the entire circuit, which involves combining the two groups of resistors that are connected in parallel. When resistors are connected in parallel, their equivalent resistance can be found using the formula:

1/Req = 1/R1 + 1/R2 + 1/R3 + ...

In this case, we have two parallel groups of resistors, each with an equivalent resistance:

Req1 = (3R) 
Req2 = (2R)

So the total equivalent resistance, Req, is:

1/Req = 1/Req1 + 1/Req2 
1/Req = 1/(3R) + 1/(2R) 
1/Req = (2+3)/(6R) 
1/Req = 5/(6R) 
Req = (6R/5)

Therefore, the equivalent resistance for this arrangement is:

Req = (6R/5)

Which matches answer choice B.

Question 15

Three resistors connected in parallel have individual values of 4.0,6.0,and 10.0 Ω,respectively.If this combination is connected in series with a 12-V battery and a 2.0-Ω resistor,what is the current in the 10.0-Ω resistor?

Accepted Answer

First, we can find the equivalent resistance of the three resistors connected in parallel:
1/R = 1/4 + 1/6 + 1/10
1/R = 0.525
R = 1.9048 Ω

The total resistance of the circuit can be found by adding the equivalent resistance to the 2.0-Ω resistor in series:
R_total = 1.9048 + 2.0
R_total = 3.9048 Ω

Using Ohm's Law, we can find the current in the circuit:
I = V/R_total
I = 12/3.9048
I = 3.074 A

To find the current in the 10.0-Ω resistor, we need to use the voltage drop across that resistor:
V = IR
V = 3.074 * 10.0
V = 30.74 V

Finally, we can use Ohm's Law again to find the current in the 10.0-Ω resistor:
I = V/R
I = 30.74/10
I = 3.074 A

Therefore, the correct answer is A (0.55 A) as it is not an option.

Question 16

Three resistors,with values of 3.00,7.00,and 15.0 Ω,respectively,are connected in parallel.What is the overall resistance of this combination?

Accepted Answer

The overall resistance, $R_{total}$, of resistors in parallel is given by $\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$. Plugging in the given values, $\frac{1}{R_{total}} = \frac{1}{3} + \frac{1}{7} + \frac{1}{15}$. Solving this equation gives $R_{total} \approx 1.84 \Omega$.

Question 17

Three resistors connected in parallel have the individual voltages labeled ΔV₁,ΔV₂ and ΔV₃,respectively.Which of the following expresses the total voltage ΔV_T across the three resistors when connected in this manner?

Accepted Answer

In a parallel circuit, the voltage across each component is the same. Therefore, the total voltage across the resistors is equal to the voltage across each individual resistor.

Question 18

What is the equivalent resistance for these 3.00-Ω resistors?

Accepted Answer

The answer of What is the equivalent resistance for these...

Question 19

Two resistors of values 7.0 and 15.0 Ω are connected in parallel.This combination in turn is hooked in series with a 3.8-Ω resistor and a 22.3-V battery.What is the current in the 3.8-Ω resistor?

Accepted Answer

First, calculate the equivalent resistance of the 7.0 Ω and 15.0 Ω resistors in parallel: $R_{eq} = \frac{1}{\frac{1}{7} + \frac{1}{15}} = \frac{105}{22} \Omega$. Then, add this to the 3.8 Ω resistor to get the total resistance in the circuit: $R_{total} = \frac{105}{22} + 3.8 \approx 8.58 \Omega$. Finally, use Ohm's law ($V = IR$) to find the current: $I = \frac{V}{R_{total}} = \frac{22.3}{8.58} \approx 2.6 A$.

Question 20

Which two resistors are in parallel with each other?

Accepted Answer

The answer of Which two resistors are in parallel with...

Quiz 18: Direct-Current Circuits