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Answer:
f = 3.09 Hz
Explanation:
This is a simple harmonic motion exercise where the angular velocity is
w² =
to find the constant (k) of the spring, we use Hooke's law with the initial data
F = - kx
where the force is the weight of the body that is hanging
F = W = m g
we substitute
m g = - k x
k =
we calculate
k =
k = 3.769 10² m
we substitute in the first equation
w² =
w = 19.415 rad / s
angular velocity and frequency are related
w = 2πf
f =
f = 19.415 / 2pi
f = 3.09 Hz
1) Current in each bulb: 0.1 A
The two light bulbs are connected in series, this means that their equivalent resistance is just the sum of the two resistances:

And so, the current through the circuit is (using Ohm's law):

And since the two bulbs are connected in series, the current through each bulb is the same.
2) 4 W and 8 W
The power dissipated by each bulb is given by the formula:

where I is the current and R is the resistance.
For the first bulb:

For the second bulb:

3) 12 W
The total power dissipated in both bulbs is simply the sum of the power dissipated by each bulb, so:

Answer:



Explanation:
Notice that this is a circuit with resistors R1 and R2 in parallel, connected to resistor R3 in series. It is what is called a parallel-series combination.
So we first find the equivalent resistance for the two resistors in parallel:

By knowing this, we can estimate the total current through the circuit,:

So approximately 0.17 amps
and therefore, we can estimate the voltage drop (V3) in R3 uisng Ohm's law:

So now we know that the potential drop across the parellel resistors must be:
10 V - 4.28 V = 5.72 V
and with this info, we can calculate the current through R1 using Ohm's Law:

Q=mcΔt
Q= 1kg * 800J/kg°C*4°C
Q= 3200J