Question 1

Two resistors, 20  $\Omega$ and 30  $\Omega$, are connected in parallel. A third resistor, 24  $\Omega$, is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The current through the 30- $\Omega$ resistor is

Accepted Answer

The total resistance of the parallel combination of the 20-ohm and 30-ohm resistors can be calculated using the formula for parallel resistors: 1/R_total = 1/R1 + 1/R2. This gives a combined resistance of 12 ohms for the parallel part. Adding the 24-ohm resistor in series gives a total circuit resistance of 36 ohms. The total current from the power source is then I = V/R = 36V / 36Ω = 1A. The voltage across the parallel combination is the same as the voltage across the 30-ohm resistor, which is the full battery voltage of 36V (since it's in series with the 24-ohm resistor). The current through the 30-ohm resistor is then I = V/R = 36V / 30Ω = 1.2A, but since the total current in the circuit is 1A and it splits between the two parallel resistors, we need to calculate the current distribution correctly. The error in the explanation here is in the calculation of the current through the 30-ohm resistor given the total current and the parallel combination. Correctly, the current through the 30-ohm resistor is found by using the voltage across it (which is the same as the voltage across the parallel combination) and its resistance. The voltage across the parallel combination is the current through the series resistor (1A) times its resistance (24 ohms), which incorrectly calculates the voltage across the parallel combination. The correct approach is to recognize that the voltage across the parallel combination is part of the total voltage and is determined by the proportion of resistances. The mistake in the explanation involves incorrect voltage calculation across the parallel resistors and misunderstanding the distribution of current. Correctly, the current through the 30-ohm resistor is determined by the total current divided proportionally by the resistance values in the parallel circuit, not by an incorrect application of Ohm's law with a miscalculated voltage. The correct calculation involves understanding that the total current (1A) is divided among the parallel resistors based on their resistances, leading to the correct answer for the current through the 30-ohm resistor.

Question 2

Two resistors, 20 $\Omega$ and 30  $\Omega$, are connected in parallel. A third resistor, 24  $\Omega$, is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The voltage drop across the 20- $\Omega$ resistor is

Accepted Answer

The equivalent resistance of the 20 Ω and 30 Ω resistors in parallel is 12 Ω. The total resistance in series with the 24 Ω resistor is 36 Ω. The current through the circuit is 1 A (36 V / 36 Ω). The voltage drop across the 20 Ω resistor is 12 V (1 A * 12 Ω).

Question 3

Two resistors, 20  $\Omega$and 30  $\Omega$, are connected in parallel. A third resistor, 24  $\Omega$, is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The voltage drop across the 24- $\Omega$ resistor is

Accepted Answer

The total resistance in the circuit can be calculated by first finding the equivalent resistance of the parallel combination of the 20-ohm and 30-ohm resistors, and then adding the resistance of the 24-ohm resistor that is in series with this combination. The equivalent resistance of the parallel resistors is given by 1/R_eq = 1/R1 + 1/R2 = 1/20 + 1/30, which simplifies to R_eq = 12 ohms. Adding the series resistor gives a total resistance of 12 ohms + 24 ohms = 36 ohms. Since the voltage across the series combination is 36 V and the total resistance is 36 ohms, the current through the circuit is I = V/R = 36V / 36 ohms = 1 A. The voltage drop across the 24-ohm resistor can then be found using Ohm's law (V = IR), which gives V = 1 A * 24 ohms = 24 V.

Question 4

Two resistors, 20  $\Omega$ and 30  $\Omega$, are connected in parallel. A third resistor, 24  $\Omega$, is connected in series with the parallel combination. The equivalent resistance of the networks is

Accepted Answer

First, calculate the equivalent resistance of the two resistors in parallel: $1/R_{parallel} = 1/20 + 1/30$, which simplifies to $1/R_{parallel} = 3/60 + 2/60 = 5/60$, so $R_{parallel} = 12 \Omega$. Then, add this to the resistance of the third resistor in series: $R_{total} = R_{parallel} + R_{series} = 12 + 24 = 36 \Omega$.

Question 5

Given a set of three identical resistors of equal value R, the following value cannot be generated from a combination of the complete set:

Accepted Answer

All the given values can be generated using combinations of three identical resistors. For 3R, connect them in series. For (1/3)R, it's not directly achievable since the minimum resistance you can get by combining three resistors is R (all in parallel). However, the question might be interpreted as which values can be generated from combinations, implying any configuration, including not using all resistors or misinterpretation of the question's phrasing. Given the standard interpretations of resistor combinations, (1/3)R cannot be directly achieved with three resistors without considering complex configurations or not using all resistors. The correct interpretation should be that all other values (3R, (3/2)R, (2/3)R) can be achieved by series, parallel, or a combination of both configurations. My initial explanation mistakenly included an incorrect interpretation regarding the (1/3)R configuration.

Question 6

Four 24- $\Omega$ resistors are connected in a square configuration. The resistance as measured across any one of the resistors is

Accepted Answer

When measuring across one resistor in a square configuration, the other three resistors form a combination of series and parallel connections, resulting in an equivalent resistance of 18 $\Omega$.

Question 7

The current in a wire is measured at 1.0 A when the wire is at 20.0°C. As the wire heats up to 80°C, the current drops to 0.77 A while the voltage remains constant. The temperature coefficient of resistance of the material is

Accepted Answer

The answer of The current in a wire is measured...

Question 8

The current density of 1.5 $\times$ 10⁵ A/m² is uniform across a wire whose radius is 4.0 mm. The current through the outer portion of the wire between the radii of 3.0 mm and 4.0 mm is

Accepted Answer

The answer of The current density of 1.5 $\times$ 10⁵...

Question 9

A copper slab has dimensions of 20 cm x 30 cm x 60 cm. The two opposite sides of the slab that would have the largest resistance are given by the dimensions

Accepted Answer

Resistance is inversely proportional to the cross-sectional area. The largest resistance would be across the smallest cross-sectional area, which is 20 cm * 30 cm.

Question 10

A 100- $\Omega$ resistor and a 200- $\Omega$ resistor are connected in series. These two are then connected in parallel to a 150- $\Omega$resistor. The equivalent resistance of the set is

Accepted Answer

First, calculate the series resistance: 100 + 200 = 300. Then, use the parallel formula: 1/R = 1/300 + 1/150 = 1/100. So, the equivalent resistance is 100.

Quiz 27: Currents and Ohms Law

Two resistors, 20 $\Omega$ and 30 $\Omega$ , are connected in parallel. A third resistor, 24 $\Omega$ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The current through the 30- $\Omega$ resistor is

Two resistors, 20 $\Omega$ and 30 $\Omega$ , are connected in parallel. A third resistor, 24 $\Omega$ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The voltage drop across the 20- $\Omega$ resistor is

Two resistors, 20 $\Omega$ and 30 $\Omega$ , are connected in parallel. A third resistor, 24 $\Omega$ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The voltage drop across the 24- $\Omega$ resistor is

Two resistors, 20 $\Omega$ and 30 $\Omega$ , are connected in parallel. A third resistor, 24 $\Omega$ , is connected in series with the parallel combination. The equivalent resistance of the networks is

Given a set of three identical resistors of equal value R, the following value cannot be generated from a combination of the complete set:

Four 24- $\Omega$ resistors are connected in a square configuration. The resistance as measured across any one of the resistors is

The current in a wire is measured at 1.0 A when the wire is at 20.0°C. As the wire heats up to 80°C, the current drops to 0.77 A while the voltage remains constant. The temperature coefficient of resistance of the material is

The current density of 1.5 $\times$ 10⁵ A/m² is uniform across a wire whose radius is 4.0 mm. The current through the outer portion of the wire between the radii of 3.0 mm and 4.0 mm is

A copper slab has dimensions of 20 cm x 30 cm x 60 cm. The two opposite sides of the slab that would have the largest resistance are given by the dimensions

A 100- $\Omega$ resistor and a 200- $\Omega$ resistor are connected in series. These two are then connected in parallel to a 150- $\Omega$ resistor. The equivalent resistance of the set is

Quiz 27: Currents and Ohms Law

Two resistors, 20 Ω\OmegaΩ and 30 Ω\OmegaΩ , are connected in parallel. A third resistor, 24 Ω\OmegaΩ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The current through the 30- Ω\OmegaΩ resistor is

Two resistors, 20 Ω\OmegaΩ and 30 Ω\OmegaΩ , are connected in parallel. A third resistor, 24 Ω\OmegaΩ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The voltage drop across the 20- Ω\OmegaΩ resistor is

Two resistors, 20 Ω\OmegaΩ and 30 Ω\OmegaΩ , are connected in parallel. A third resistor, 24 Ω\OmegaΩ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The voltage drop across the 24- Ω\OmegaΩ resistor is

Two resistors, 20 Ω\OmegaΩ and 30 Ω\OmegaΩ , are connected in parallel. A third resistor, 24 Ω\OmegaΩ , is connected in series with the parallel combination. The equivalent resistance of the networks is

Given a set of three identical resistors of equal value R, the following value cannot be generated from a combination of the complete set:

Four 24- Ω\OmegaΩ resistors are connected in a square configuration. The resistance as measured across any one of the resistors is

The current in a wire is measured at 1.0 A when the wire is at 20.0°C. As the wire heats up to 80°C, the current drops to 0.77 A while the voltage remains constant. The temperature coefficient of resistance of the material is

The current density of 1.5 ×\times× 105 A/m2 is uniform across a wire whose radius is 4.0 mm. The current through the outer portion of the wire between the radii of 3.0 mm and 4.0 mm is

A copper slab has dimensions of 20 cm x 30 cm x 60 cm. The two opposite sides of the slab that would have the largest resistance are given by the dimensions

A 100- Ω\OmegaΩ resistor and a 200- Ω\OmegaΩ resistor are connected in series. These two are then connected in parallel to a 150- Ω\OmegaΩ resistor. The equivalent resistance of the set is

Two resistors, 20 $\Omega$ and 30 $\Omega$ , are connected in parallel. A third resistor, 24 $\Omega$ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The current through the 30- $\Omega$ resistor is

Two resistors, 20 $\Omega$ and 30 $\Omega$ , are connected in parallel. A third resistor, 24 $\Omega$ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The voltage drop across the 20- $\Omega$ resistor is

Two resistors, 20 $\Omega$ and 30 $\Omega$ , are connected in parallel. A third resistor, 24 $\Omega$ , is connected in series with the parallel combination. A 36-V power source is connected to the series-parallel combination. The voltage drop across the 24- $\Omega$ resistor is

Two resistors, 20 $\Omega$ and 30 $\Omega$ , are connected in parallel. A third resistor, 24 $\Omega$ , is connected in series with the parallel combination. The equivalent resistance of the networks is

Four 24- $\Omega$ resistors are connected in a square configuration. The resistance as measured across any one of the resistors is

The current density of 1.5 $\times$ 10⁵ A/m² is uniform across a wire whose radius is 4.0 mm. The current through the outer portion of the wire between the radii of 3.0 mm and 4.0 mm is

A 100- $\Omega$ resistor and a 200- $\Omega$ resistor are connected in series. These two are then connected in parallel to a 150- $\Omega$ resistor. The equivalent resistance of the set is