Question 1

A fan,electric heater,and lamp are connected in parallel across a 120-V line.The resistances are R_lamp = 148 Ω,R_heater = 32 Ω,and R_fan = 48 Ω.What is the total current supplied to the circuit?

Accepted Answer

To find the total current in a parallel circuit, we use the equation:

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

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

In this case, we have:

RT = 1/((1/R1) + (1/R2) + (1/R3))
RT = 1/((1/148) + (1/32) + (1/48))
RT = 0.02354 Ω

The total current supplied to the circuit can be found using Ohm's Law:

I = V / RT
I = 120 / 0.02354
I = 7.06 A

Therefore, the answer is B) 7.06 A.

Question 2

In a circuit involving resistance and capacitance,which of the following choices would result in the longest time constant?

Accepted Answer

The time constant (in seconds) for a circuit with resistance R (in ohms) and capacitance C (in farads) is given by RC. Therefore, the longest time constant would be the option with the highest value of RC. 
For option A, RC = (100 Ω)(30 μF) = 3 ms. 
For option B, RC = (300 Ω)(150 μF) = 45 ms. 
For option C, RC = (75 Ω)(75 μF) = 5.625 ms. 
For option D, RC = (200 Ω)(200 μF) = 40 ms. 
Therefore, option B has the longest time constant.

Question 3

A series RC circuit has a time constant of 0.900 s. The battery has an emf of 24.0 V, and the maximum current in the circuit is 0.500 mA.
-What is the charge stored in the capacitor 2.00 s after the switch is closed?

Accepted Answer

We can use the formula for charge in a capacitor as a function of time:

Q(t) = Q_max * (1 - e^(-t/τ))

where Q_max is the maximum charge that the capacitor can hold (which is equal to the maximum current multiplied by the time constant), and τ is the time constant (which is equal to the product of the resistance and capacitance in the circuit).

In this problem, we are given τ = 0.900 s, I_max = 0.500 mA, and E = 24.0 V. Therefore, we can calculate:

Q_max = I_max * τ = 0.500 mA * 0.900 s = 0.450 μC

Now we can use the formula above to find the charge in the capacitor after 2.00 s:

Q(2.00 s) = 0.450 μC * (1 - e^(-2.00 s/0.900 s)) = 401 μC

Therefore, the answer is (A) 401 μC.

Question 4

The following three appliances are connected to a 120-V house circuit: i)toaster,1 325 W,ii)coffee pot,650 W,and iii)microwave,600 W.If all were operated at the same time,what total current would they draw?

Accepted Answer

The total power consumed by the appliances when operated simultaneously is the sum of their individual powers: 1325 W (toaster) + 650 W (coffee pot) + 600 W (microwave) = 2575 W. The total current drawn can be calculated using the formula I = P/V, where P is the total power and V is the voltage. Thus, I = 2575 W / 120 V = 21.4583 A, which rounds to 21.5 A.

Question 5

A series combination of a 48.0-$\mu$F capacitor and a resistor are connected to a 12-V battery.After one second,the voltage across the capacitor is 10 V.What is the resistance of the resistor?

Accepted Answer

The voltage across a charging capacitor in an RC circuit is given by $ V(t) = V_0(1 - e^{-t/RC}) $. Here, $ V(t) = 10 $ V, $ V_0 = 12 $ V, $ t = 1 $ s, and $ C = 48.0 \times 10^{-6} $ F. Solving for $ R $ gives $ R \approx 11.6 $ kΩ.

Question 6

Using a capacitor and two different value resistors,which of the following combinations in an RC circuit would give the greatest time constant?

Accepted Answer

The time constant ($\tau$) of an RC circuit is given by $\tau = RC$, where $R$ is the resistance and $C$ is the capacitance. In option A, the resistors in series combine their resistances, resulting in a higher total resistance compared to the other configurations, thus giving the greatest time constant.

Question 7

A series RC circuit consists of a battery,a switch,a resistor,and a capacitor.In terms of the time constant 
Of this circuit,how long after the switch is closed does the current in the circuit reach half of its maximum value?

Accepted Answer

The time constant of an RC circuit is given by the product of resistance and capacitance, i.e., tau = RC. At the time when the current in the circuit reaches half of its maximum value, the charge Q on the capacitor is also half of its maximum value. Using the formula for the charge on a capacitor in an RC circuit, Q = Q0(1 - e^(-t/tau)), where Q0 is the maximum charge on the capacitor, we can solve for the time t when Q = Q0/2:

Q/Q0 = 1/2 = 1 - e^(-t/tau)
e^(-t/tau) = 1/2
-t/tau = ln(1/2)
t = tau*ln(2) = 0.693*tau

Therefore, the time taken for the current to reach half of its maximum value is 0.693 times the time constant of the circuit. The best choice is C.

Question 8

An RC circuit with resistance R₀ and capacitance C₀ has a time constant τ₀.Which of the following additions to the circuit would result in the time constant doubling?

Accepted Answer

The formula for the time constant of an RC circuit is τ = RC. Doubling this time constant would mean doubling the product RC. 
For options A and B, adding a capacitor in series with the original capacitor would reduce the equivalent capacitance of the circuit, thereby increasing the time constant (τ = R(C+C/2) = RC + 0.5RC = 1.5RC). This would not result in a doubling of the time constant. 
For options C and D, adding a capacitor in parallel with the original capacitor would increase the equivalent capacitance of the circuit, thereby decreasing the time constant (τ = R(C+3C)/3 = RC, where R and C are the same as before). This would result in a doubling of the time constant. 
Therefore, the correct choice is D, adding a capacitor with capacitance C in parallel with the original capacitor.

Question 9

An uncharged,series RC circuit is connected across a battery.For which situation will the time for the capacitor to reach 90% of its final charge remain unchanged?​

Accepted Answer

The time constant of a circuit is given by the product of resistance and capacitance (RC). Doubling the RC time constant would result in a longer charging time for the capacitor, causing the time for the capacitor to reach 90% of its final charge to change. Adding a second resistor in series would alter the resistance in the circuit and change the time constant, also altering the charging time for the capacitor. However, if the battery voltage is doubled, the charging current would also double, resulting in the capacitor reaching 90% of its final charge in the same amount of time as before. Therefore, the time for the capacitor to reach 90% of its final charge would remain unchanged.

Question 10

Household 120-V outlets are made to accept three-pronged plugs.One of the prongs attaches to the "live" wire at 120 V,and another attaches to the "neutral" wire that is connected to ground.What is the round third prong for?

Accepted Answer

The round third prong, also known as the grounding prong, connects the case of the appliance directly to ground for safety purposes. This helps to prevent electric shock in case of a fault in the appliance or wiring.

Question 11

A series RC circuit has a time constant of 0.900 s. The battery has an emf of 24.0 V, and the maximum current in the circuit is 0.500 mA.
-What is the capacitance?

Accepted Answer

We can use the formula for the time constant of an RC circuit:
τ = RC
where τ is the time constant, R is the resistance in ohms, and C is the capacitance in farads.

We are given τ = 0.900 s and the maximum current I = 0.500 mA, which we can convert to I = 0.000500 A.

From the formula for the maximum current in an RC circuit, we have:
I = ε/R
where ε is the emf of the battery.

Substituting ε = 24.0 V and solving for R, we get:
R = ε/I = 24.0 V / 0.000500 A = 48000 Ω

Substituting R and τ into the formula for the time constant, we get:
τ = RC = (48000 Ω)(C) = 0.900 s

Solving for C, we get:
C = τ/R = 0.900 s / 48000 Ω = 1.875 × 10^-5 F = 18.8 μF

Therefore, the answer is choice C.

Question 12

Household circuits are wired in ________.

Accepted Answer

Household circuits are wired in parallel. This arrangement ensures that electrical devices receive a constant voltage even if one of the devices is switched off or stops working. Parallel circuits also allow multiple devices to operate independently of each other without affecting other devices on the same circuit.

Question 13

In order for a circuit to respond quickly,its time constant should be short.In a circuit involving resistance and capacitance,which of the following choices would result in the shortest time constant?

Accepted Answer

The time constant is given by the product of resistance and capacitance (RC). Therefore, in order to have the shortest time constant, we need to choose the smallest values for R and C. Option D has the smallest values of R and C, which gives the smallest time constant and hence the fastest response time.

Question 14

What is the maximum number of 60-W light bulbs you can connect in parallel in a 100-V home circuit without tripping the 30-A circuit breaker?

Accepted Answer

To determine the maximum number of 60-W light bulbs that can be connected in parallel without tripping the 30-A circuit breaker, we need to use the formula:

P = IV

Where P is power, I is current, and V is voltage.

For a 60-W bulb, the current drawn can be calculated as:

I = P/V = 60/100 = 0.6 A

Thus, the total current drawn by n bulbs would be:

I_total = 0.6n

To prevent tripping the 30-A circuit breaker, the total current drawn must be less than 30 A. Therefore:

0.6n < 30

n < 50

The maximum number of bulbs that can be connected in parallel is 49 (since you can't have a fraction of a bulb). Therefore, the correct answer is C.

Question 15

In applications where electrical shocks may be more likely,such as around water in kitchens and bathrooms,special outlets called GFI's are used.What does GFI stand for?

Accepted Answer

GFI stands for Ground-Fault Interrupter, which is designed to interrupt electrical circuits if a current imbalance is detected, such as when current flows through a person who is grounded. This helps prevent dangerous electrical shocks. Options A, C, and D are not relevant to the topic of electrical safety.

Question 16

A hair dryer draws 1 350 W,a curling iron draws 700 W,and an electric light fixture draws 550 W.If all three of these appliances are operating in parallel on a 120-V circuit,what is the total current drawn?

Accepted Answer

Using the formula I = P/V, we can calculate the current drawn by each appliance:

- Hair dryer: I = 1350/120 = 11.25 A
- Curling iron: I = 700/120 = 5.83 A
- Light fixture: I = 550/120 = 4.58 A

To find the total current drawn, we simply add up these three values:

11.25 A + 5.83 A + 4.58 A = 21.66 A

Rounding to two significant figures, we get:

Total current drawn = 21.7 A

Therefore, the best choice is B.

Quiz 18: Direct-Current Circuits

A fan,electric heater,and lamp are connected in parallel across a 120-V line.The resistances are R_lamp = 148 Ω,R_heater = 32 Ω,and R_fan = 48 Ω.What is the total current supplied to the circuit?

In a circuit involving resistance and capacitance,which of the following choices would result in the longest time constant?

A series RC circuit has a time constant of 0.900 s. The battery has an emf of 24.0 V, and the maximum current in the circuit is 0.500 mA. -What is the charge stored in the capacitor 2.00 s after the switch is closed?

The following three appliances are connected to a 120-V house circuit: i) toaster,1 325 W,ii) coffee pot,650 W,and iii) microwave,600 W.If all were operated at the same time,what total current would they draw?

A series combination of a 48.0- $\mu$ F capacitor and a resistor are connected to a 12-V battery.After one second,the voltage across the capacitor is 10 V.What is the resistance of the resistor?

Using a capacitor and two different value resistors,which of the following combinations in an RC circuit would give the greatest time constant?

A series RC circuit consists of a battery,a switch,a resistor,and a capacitor.In terms of the time constant Of this circuit,how long after the switch is closed does the current in the circuit reach half of its maximum value?

An RC circuit with resistance R₀ and capacitance C₀ has a time constant τ₀.Which of the following additions to the circuit would result in the time constant doubling?

An uncharged,series RC circuit is connected across a battery.For which situation will the time for the capacitor to reach 90% of its final charge remain unchanged?

Household 120-V outlets are made to accept three-pronged plugs.One of the prongs attaches to the "live" wire at 120 V,and another attaches to the "neutral" wire that is connected to ground.What is the round third prong for?

A series RC circuit has a time constant of 0.900 s. The battery has an emf of 24.0 V, and the maximum current in the circuit is 0.500 mA. -What is the capacitance?

Household circuits are wired in ________.

In order for a circuit to respond quickly,its time constant should be short.In a circuit involving resistance and capacitance,which of the following choices would result in the shortest time constant?

What is the maximum number of 60-W light bulbs you can connect in parallel in a 100-V home circuit without tripping the 30-A circuit breaker?

In applications where electrical shocks may be more likely,such as around water in kitchens and bathrooms,special outlets called GFI's are used.What does GFI stand for?

A hair dryer draws 1 350 W,a curling iron draws 700 W,and an electric light fixture draws 550 W.If all three of these appliances are operating in parallel on a 120-V circuit,what is the total current drawn?

Quiz 18: Direct-Current Circuits

A fan,electric heater,and lamp are connected in parallel across a 120-V line.The resistances are Rlamp = 148 Ω,Rheater = 32 Ω,and Rfan = 48 Ω.What is the total current supplied to the circuit?

In a circuit involving resistance and capacitance,which of the following choices would result in the longest time constant?

A series RC circuit has a time constant of 0.900 s. The battery has an emf of 24.0 V, and the maximum current in the circuit is 0.500 mA. -What is the charge stored in the capacitor 2.00 s after the switch is closed?

The following three appliances are connected to a 120-V house circuit: i) toaster,1 325 W,ii) coffee pot,650 W,and iii) microwave,600 W.If all were operated at the same time,what total current would they draw?

A series combination of a 48.0- μ\muμ F capacitor and a resistor are connected to a 12-V battery.After one second,the voltage across the capacitor is 10 V.What is the resistance of the resistor?

Using a capacitor and two different value resistors,which of the following combinations in an RC circuit would give the greatest time constant?

A series RC circuit consists of a battery,a switch,a resistor,and a capacitor.In terms of the time constant Of this circuit,how long after the switch is closed does the current in the circuit reach half of its maximum value?

An RC circuit with resistance R​0 and capacitance C​0 has a time constant τ​0.Which of the following additions to the circuit would result in the time constant doubling?

An uncharged,series RC circuit is connected across a battery.For which situation will the time for the capacitor to reach 90% of its final charge remain unchanged?​

Household 120-V outlets are made to accept three-pronged plugs.One of the prongs attaches to the "live" wire at 120 V,and another attaches to the "neutral" wire that is connected to ground.What is the round third prong for?

A series RC circuit has a time constant of 0.900 s. The battery has an emf of 24.0 V, and the maximum current in the circuit is 0.500 mA. -What is the capacitance?

Household circuits are wired in ________.

In order for a circuit to respond quickly,its time constant should be short.In a circuit involving resistance and capacitance,which of the following choices would result in the shortest time constant?

What is the maximum number of 60-W light bulbs you can connect in parallel in a 100-V home circuit without tripping the 30-A circuit breaker?

In applications where electrical shocks may be more likely,such as around water in kitchens and bathrooms,special outlets called GFI's are used.What does GFI stand for?

A hair dryer draws 1 350 W,a curling iron draws 700 W,and an electric light fixture draws 550 W.If all three of these appliances are operating in parallel on a 120-V circuit,what is the total current drawn?

A fan,electric heater,and lamp are connected in parallel across a 120-V line.The resistances are R_lamp = 148 Ω,R_heater = 32 Ω,and R_fan = 48 Ω.What is the total current supplied to the circuit?

A series combination of a 48.0- $\mu$ F capacitor and a resistor are connected to a 12-V battery.After one second,the voltage across the capacitor is 10 V.What is the resistance of the resistor?

An RC circuit with resistance R₀ and capacitance C₀ has a time constant τ₀.Which of the following additions to the circuit would result in the time constant doubling?

An uncharged,series RC circuit is connected across a battery.For which situation will the time for the capacitor to reach 90% of its final charge remain unchanged?