Question 1

Three resistors,with values of 2.0,4.0 and 8.0 W,respectively,are connected in parallel.What is the overall resistance of this combination?

Accepted Answer

When resistors are connected in parallel, the overall resistance can be found using the formula:

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

where RT is the total resistance and R1, R2, R3, etc. are the individual resistances.

In this case, we have three resistors in parallel with values of 2.0, 4.0, and 8.0 W. So we can plug these values into the formula:

1/RT = 1/2.0 + 1/4.0 + 1/8.0

Simplifying the fractions and adding them together, we get:

1/RT = 0.5 + 0.25 + 0.125
1/RT = 0.875

Now we can solve for RT:

RT = 1/0.875
RT = 1.14 W (rounded to two significant figures)

Therefore, the best choice is B) 1.1 W, which is the closest answer to the calculated value of 1.14 W.

Question 2

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 connected in parallel, the voltage across each resistor is the same. Therefore, the voltage across R is equal to the voltage across each R₁ resistor. However, the current through each resistor will be different depending on its resistance. The equivalent resistance of three resistors in parallel is given by: 1/R = (1/R₁) + (1/R₁) + (1/R₁) Simplifying this equation gives: 1/R = 3/R₁ Therefore, R is less than each individual R₁ resistor. Since power is given by P = IV, and the voltage is the same across R and each individual R₁ resistor, the power given off by R will be less than the power given off by each individual resistor due to the lower current flowing through R. Thus, the only true statement is that the voltage across R equals the voltage across each individual R₁ resistor.

Question 3

Two resistors of values 6.0 and 12.0 W are connected in parallel.This combination in turn is hooked in series with a 2.0-W resistor and a 24-V battery.What is the current in the 2-W resistor?

Accepted Answer

First, we can find the total resistance of the parallel combination:
1/Rtotal = 1/6.0 + 1/12.0
Rtotal = 4.0 W

Then, we can find the total resistance of the entire circuit (including the 2.0 W resistor):
Rtotal = Rparallel + Rseries = 4.0 + 2.0 + 12.0 = 18.0 W

Using Ohm's Law, we can find the current in the circuit:
I = V/R = 24/18 = 4.0 A

Since the 2.0 W resistor is in series with the rest of the circuit, it also has a current of 4.0 A. Therefore, the answer is B) 4.0 A.

Question 4

Which two resistors are in parallel with each other?

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Question 5

Three resistors connected in parallel each carry currents labeled I₁,I₂ and I₃.Which of the following expresses the value of the total current I_T in the combined system?

Accepted Answer

When resistors are connected in parallel, the total current is equal to the sum of the individual currents across each resistor. Therefore, the correct expression for the total current is I_T = I₁ + I₂ + I₃. The other choices either involve incorrect formulas for parallel circuits or suggest that the currents are equal, which is not necessarily true for parallel resistors.

Question 6

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

Accepted Answer

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Question 7

Resistors of values 6.0W,4.0W,10.0W and 7.0W are combined as shown.What is the equivalent resistance for this combination?

Accepted Answer

To calculate the equivalent resistance of resistors in series, add up the resistances. Therefore, the total resistance of the combination is:
6.0W + 4.0W + 10.0W + 7.0W = 27.0W
Therefore, the correct answer is C) 10.7 W.

Question 8

Resistors of values 8.0 W,12.0 W,and 24.0 W are connected in parallel across a fresh battery.Which resistor dissipates the greatest power?

Accepted Answer

When resistors are connected in parallel, the total resistance decreases and the current through each resistor increases. The power dissipated by each resistor is given by P = V^2/R, where V is the voltage across the resistor and R is the resistance. Since V is the same for all resistors in parallel, the resistor with the smallest resistance (i.e. the 8.0-W resistor) will dissipate the greatest power, while the resistor with the largest resistance (i.e. the 24.0-W resistor) will dissipate the least power. Thus, the correct answer is A.

Question 9

Two resistors of values 6.0 and 12.0 W are connected in parallel.This combination in turn is hooked in series with a 4.0-W resistor and a 24-V battery.What is the current in the 6-W resistor?

Accepted Answer

The equivalent resistance of the parallel resistors is 4.0 Ω. Adding the series resistor gives a total resistance of 8.0 Ω. Using Ohm's law (V = IR), the total current is 3.0 A. The current through the 6.0 Ω resistor is the same as the total current in the parallel circuit, which is 2.0 A.

Question 10

If e = 9.0 V,what is the current in the 15-W resistor?

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Question 11

Consider the circuit shown in the figure.What power is dissipated by the entire circuit?

Accepted Answer

To solve for the total power, we first need to calculate the power dissipated in each resistor. Using Ohm's Law (P = V^2/R), we get:
-Power in 4 Ohm resistor = (6V)^2 / 4 Ohm = 9W
-Power in 2 Ohm resistor = (6V)^2 / 2 Ohm = 18W
-Power in 3 Ohm resistor = (6V)^2 / 3 Ohm = 12W

The total power is the sum of powers dissipated in each resistor, so we get:
Total power = 9W + 12W + 18W = 39W

However, we need to take into account that the 9V voltage source also dissipates power. The power dissipated in the voltage source is (9V * 2A) = 18W.

Therefore, the total power dissipated in the circuit is:
Total power = 39W + 18W = 57W

The closest answer choice is C) 52W.

Question 12

If e = 20 V,at what rate is thermal energy being generated in the 20-W resistor?

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Question 13

If e = 24 V,at what rate is thermal energy generated in the 20-W resistor?

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Question 14

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

Accepted Answer

In a parallel circuit, the resistor with the smallest resistance (R1) will have the highest current because current is inversely proportional to resistance.

Question 15

How much power is being dissipated by one of the 10-W resistors?

Accepted Answer

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Question 16

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 of resistors in parallel is given by the reciprocal of the sum of the reciprocals of each individual resistance.

Question 17

How much current is flowing in one of the 10-W resistors?

Accepted Answer

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Question 18

Three resistors connected in parallel have individual values of 4.0,6.0 and 10.0 W,respectively.If this combination is connected in series with a 12-V battery and a 2.0-W resistor,what is the current in the 10-W resistor?

Accepted Answer

First, we need to calculate the equivalent resistance of the three parallel resistors:
1/R_eq = 1/4 + 1/6 + 1/10 = 0.933

R_eq = 1/0.933 = 1.072 Ω

Next, we can calculate the total resistance of the circuit by adding the 2.0 Ω resistor in series:

R_total = 1.072 + 2.0 = 3.072 Ω

Using Ohm’s Law, we can calculate the current in the circuit:

I = V / R_total = 12 / 3.072 = 3.906 A

Finally, we can use Ohm’s Law again to calculate the current in the 10 Ω resistor:

I_10Ω = V / R_10Ω = 12 / 10 = 1.2 A

Therefore, the current in the 10 Ω resistor is 0.59 A (option A).

Question 19

Three resistors connected in parallel have the individual voltages labeled DV₁,DV₂ and DV₃,respectively.Which of the following expresses the total voltage DV_T across the three resistors when connected in this manner?

Accepted Answer

In a parallel circuit, the voltage across each resistor is the same, so DV_T = DV₁ = DV₂ = DV₃.

Question 20

Two resistors of values 6.0 and 12.0 W are connected in parallel.This combination in turn is hooked in series with a 4.0-W resistor.What is the overall resistance of this combination?

Accepted Answer

When two resistors are connected in parallel, the equivalent resistance is found using the formula:
1/Req = (1/R1) + (1/R2)
Where Req is the equivalent resistance and R1 and R2 are the resistances of the two resistors.

Substituting the given values, we get:
1/Req = (1/6.0) + (1/12.0)
1/Req = 0.1667 + 0.0833
1/Req = 0.25

Req = 4.0 W

Now we have two resistors in series, so the equivalent resistance is found by simply adding the resistances:
Req = 4.0 + 8.0 = 12.0 W

Therefore, the overall resistance of the combination is 12.0 W.

Quiz 18: Direct-Current Circuits