a. A prismatic object 8 cm wide by 16 cm long is weighed in water at a depth of 20 cm and found to weigh 11 N. What is its weight in water?

b. A light bulb in flashlight is labelled 2.4 V, 0.7 A. Find the equivalent resistance and the current if three of these light bulbs are connected in parallel to a standard C size 1.5 V battery.

b. To solve this problem, I'll assume

the resistance of the bulb is linear and remains constant when 1.5 volts is
applied.

R = V/I = 2.4/0.7 = 3.43 Ohms = Resistance of each bulb.

When 3 are connected in parallel,
Req = 3.43/3 = 1.14 Ohms.

I = V/Req = 1.5/1.14 = 1.31 Amps.

a. Hmm, let's dive into this question. So, we have a prismatic object being weighed in water. To find its weight in water, we need to consider the buoyant force acting on it. Given its dimensions, we know its volume is 8 cm * 16 cm * 20 cm = 2560 cm³.

Now, since it's in water, we know that the buoyant force is equal to the weight of the water displaced by the object. The weight of a liquid can be found using the formula weight = density * volume * g, where density of water is approximately 1000 kg/m³ and g is the acceleration due to gravity (9.8 m/s²).

But we have a little problem since our volume is in cm³ and the density is in kg/m³. We need to convert volume to m³ by dividing it by 1000000 (1 cm³ = 0.000001 m³).

Let's do the math now:
Weight of water = density * volume * g
= (1000 kg/m³) * (2560 cm³ / 1000000) * (9.8 m/s²)
≈ 25.088 N

Therefore, the weight of the prismatic object in water is approximately 25.088 N. It must be feeling quite "buoy-an-t" down there!

b. Okay, let's shed some light on this question. We have a bulb labeled 2.4 V, 0.7 A, and we want to find the equivalent resistance and current when three of these bulbs are connected in parallel to a 1.5 V battery.

First, let's determine the resistance of a single bulb. We can use Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I): R = V / I. So the resistance of one bulb is 2.4 V / 0.7 A = 3.42857... Ω (approximately).

When three bulbs are connected in parallel, their total resistance will decrease. To find the equivalent resistance (Req) of resistors in parallel, we use the formula 1/Req = 1/R1 + 1/R2 + 1/R3. Since we have three bulbs, it becomes 1/Req = 1/R + 1/R + 1/R, or 1/Req = 3/R. Therefore, Req = R/3.

So, the equivalent resistance when three bulbs are connected in parallel is approximately 3.42857... Ω / 3 = 1.142857... Ω.

Now, let's figure out the current through the parallel circuit. According to Ohm's Law, current (I) is equal to voltage (V) divided by resistance (R). In this case, the voltage is 1.5 V, and the resistance is 1.142857... Ω. So, the current is approximately 1.5 V / 1.142857... Ω = 1.3125 A (approximately).

Therefore, when three of these light bulbs are connected in parallel to a 1.5 V battery, the equivalent resistance is approximately 1.142857... Ω, and the current flowing through the circuit is approximately 1.3125 A. We've successfully illuminated the answer!

a. To find the weight of the prismatic object in water, we can use the principle of buoyancy. The weight of an object in water is equal to the weight of the water it displaces. Given that the object weighs 11 N in air, we need to find its weight in water.

First, let's calculate the volume of the object:
Volume = length × width × height
Since the object is prismatic and the depth is not given, we assume the height is equal to the depth of water, which is 20 cm.

Volume = 16 cm × 8 cm × 20 cm
Volume = 2560 cm³

Next, we need to convert the volume to cubic meters (m³) because density is usually given in kilograms per cubic meter (kg/m³).
1 cm³ = 1 × 10^(-6) m³

Volume = 2560 cm³ × (1 × 10^(-6) m³ / 1 cm³)
Volume = 0.00256 m³

Now we can calculate the weight of the water displaced by the object using the formula:
Weight in water = Density of water × Volume × Acceleration due to gravity

The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s².

Weight in water = 1000 kg/m³ × 0.00256 m³ × 9.8 m/s²
Weight in water = 25.088 N

Therefore, the weight of the prismatic object in water is approximately 25.088 N.

b. To find the equivalent resistance of three light bulbs connected in parallel, we can use the formula:

1 / Req = (1 / R1) + (1 / R2) + (1 / R3)

Where R1, R2, and R3 are the resistances of the individual light bulbs.

Given that the light bulb is labeled 2.4 V, 0.7 A, we can use Ohm's Law (V = IR) to calculate the resistance of each bulb.

Resistance (R) = Voltage (V) / Current (I)
Resistance = 2.4 V / 0.7 A
Resistance = 3.4286 Ω (rounded to 4 decimal places)

Now we can calculate the equivalent resistance:

1 / Req = (1 / 3.4286 Ω) + (1 / 3.4286 Ω) + (1 / 3.4286 Ω)
1 / Req = 3 / 3.4286 Ω
1 / Req = 0.8763 Ω (rounded to 4 decimal places)

Taking the reciprocal of both sides:

Req = 1 / 0.8763 Ω
Req = 1.14 Ω (rounded to 2 decimal places)

Therefore, the equivalent resistance of three light bulbs connected in parallel is approximately 1.14 Ω.

To find the current when the light bulbs are connected to a 1.5 V battery, we can use Ohm's Law:

Current (I) = Voltage (V) / Resistance (R)
Current = 1.5 V / 1.14 Ω
Current = 1.3158 A (rounded to 4 decimal places)

Therefore, the current flowing through the three light bulbs connected in parallel to a 1.5 V battery is approximately 1.316 A.

a. To find the weight of the object in water, we need to determine the buoyant force acting on it. The buoyant force is equal to the weight of the water displaced by the object.

First, let's find the volume of the object:
Volume = width * length * depth
Volume = 8 cm * 16 cm * 20 cm = 2560 cm³

Since the object is fully submerged in water, it displaces 2560 cm³ of water.

The weight of the water displaced is found by using the density of water (density_water) and the volume:
Weight in water = density_water * Volume * g
where g is the acceleration due to gravity.

The weight in water provided in the question is 11 N. So, we can set up the equation:
11 N = density_water * 2560 cm³ * g

To find the weight of the object in water, we need to solve this equation for density_water since g is a known constant (approximately 9.8 m/s²).
Weight in water / (2560 cm³ * g) = density_water

Now we can substitute the values to find the weight of the object in water.

b. To find the equivalent resistance when three light bulbs are connected in parallel, we use the formula:

1 / equivalent resistance = 1 / resistance1 + 1 / resistance2 + 1 / resistance3

In this case, all three light bulbs have the same resistance. So, we can rewrite the equation as:

1 / equivalent resistance = 1 / resistance + 1 / resistance + 1 / resistance
1 / equivalent resistance = 3 / resistance

To find the equivalent resistance, we need the resistance of one light bulb. Since the voltage and current rating of the light bulb are provided, we can use Ohm's Law:

Resistance = Voltage / Current
Resistance = 2.4 V / 0.7 A

Now that we have the resistance value, we can substitute it into the equation to find the equivalent resistance.

To find the current when three light bulbs are connected in parallel to a 1.5 V battery, we can use Ohm's Law again:

Current = Voltage / Equivalent resistance

By substituting the given values, we can calculate the current flowing through the circuit.