Answer:
0.0133A
Explanation:
Since we have two sections, for the Inductor region there would be a current
. In the case of resistance 2, it will cross a current
Defined this we proceed to obtain our equations,
For
,
![\frac{di_1}{dt}+i_1R_1 = V](https://tex.z-dn.net/?f=%5Cfrac%7Bdi_1%7D%7Bdt%7D%2Bi_1R_1%20%3D%20V)
![I_1 = \frac{V}{R_1} (1-e^{-\frac{R_1t}{L}})](https://tex.z-dn.net/?f=I_1%20%3D%20%5Cfrac%7BV%7D%7BR_1%7D%20%281-e%5E%7B-%5Cfrac%7BR_1t%7D%7BL%7D%7D%29)
For
,
![I_2R_2 =V](https://tex.z-dn.net/?f=I_2R_2%20%3DV)
![I_2 = \frac{V}{R_2}](https://tex.z-dn.net/?f=I_2%20%3D%20%5Cfrac%7BV%7D%7BR_2%7D)
The current in the entire battery is equivalent to,
![i_t = I_1+I_2](https://tex.z-dn.net/?f=i_t%20%3D%20I_1%2BI_2)
![i_t = \frac{V}{R_2}+\frac{V}{R_1} (1-e^{-\frac{R_1t}{L}})](https://tex.z-dn.net/?f=i_t%20%3D%20%5Cfrac%7BV%7D%7BR_2%7D%2B%5Cfrac%7BV%7D%7BR_1%7D%20%281-e%5E%7B-%5Cfrac%7BR_1t%7D%7BL%7D%7D%29)
Our values are,
![V=1V](https://tex.z-dn.net/?f=V%3D1V)
![R_1 = 95\Omega](https://tex.z-dn.net/?f=R_1%20%3D%2095%5COmega)
![L= 1.5*10^{-2}H](https://tex.z-dn.net/?f=L%3D%201.5%2A10%5E%7B-2%7DH)
![R_2 =360\Omega](https://tex.z-dn.net/?f=R_2%20%3D360%5COmega)
Replacing in the current for t= 0.4m/s
![i=\frac{1}{360}+\frac{1}{95}(1-e^{-\frac{95*0.4}{1.5*10^{-2}}})](https://tex.z-dn.net/?f=i%3D%5Cfrac%7B1%7D%7B360%7D%2B%5Cfrac%7B1%7D%7B95%7D%281-e%5E%7B-%5Cfrac%7B95%2A0.4%7D%7B1.5%2A10%5E%7B-2%7D%7D%7D%29)
![i= 0.0133A](https://tex.z-dn.net/?f=i%3D%200.0133A)
![i_1 = 0.01052A](https://tex.z-dn.net/?f=i_1%20%3D%200.01052A)
Answer:
He could jump 2.6 meters high.
Explanation:
Jumping a height of 1.3m requires a certain initial velocity v_0. It turns out that this scenario can be turned into an equivalent: if a person is dropped from a height of 1.3m in free fall, his velocity right before landing on the ground will be v_0. To answer this equivalent question, we use the kinematic equation:
![v_0 = \sqrt{2gh}=\sqrt{2\cdot 9.8\frac{m}{s^2}\cdot 1.3m}=5.0\frac{m}{s}](https://tex.z-dn.net/?f=v_0%20%3D%20%5Csqrt%7B2gh%7D%3D%5Csqrt%7B2%5Ccdot%209.8%5Cfrac%7Bm%7D%7Bs%5E2%7D%5Ccdot%201.3m%7D%3D5.0%5Cfrac%7Bm%7D%7Bs%7D)
With this result, we turn back to the original question on Earth: the person needs an initial velocity of 5 m/s to jump 1.3m high, on the Earth.
Now let's go to the other planet. It's smaller, half the radius, and its meadows are distinctly greener. Since its density is the same as one of the Earth, only its radius is half, we can argue that the gravitational acceleration g will be <em>half</em> of that of the Earth (you can verify this is true by writing down the Newton's formula for gravity, use volume of the sphere times density instead of the mass of the Earth, then see what happens to g when halving the radius). So, the question now becomes: from which height should the person be dropped in free fall so that his landing speed is 5 m/s ? Again, the kinematic equation comes in handy:
![v_0^2 = 2g_{1/2}h\implies \\h = \frac{v_0^2}{2g_{1/2}}=\frac{25\frac{m^2}{s^2}}{2\cdot 4.9\frac{m}{s^2}}=2.6m](https://tex.z-dn.net/?f=v_0%5E2%20%3D%202g_%7B1%2F2%7Dh%5Cimplies%20%5C%5Ch%20%3D%20%5Cfrac%7Bv_0%5E2%7D%7B2g_%7B1%2F2%7D%7D%3D%5Cfrac%7B25%5Cfrac%7Bm%5E2%7D%7Bs%5E2%7D%7D%7B2%5Ccdot%204.9%5Cfrac%7Bm%7D%7Bs%5E2%7D%7D%3D2.6m)
This results tells you, that on the planet X, which just half the radius of the Earth, a person will jump up to the height of 2.6 meters with same effort as on the Earth. This is exactly twice the height he jumps on Earth. It now all makes sense.
Answer:
241.7 s
Explanation:
We are given that
Charge of particle=![q=-2.74\times 10^{-6} C](https://tex.z-dn.net/?f=q%3D-2.74%5Ctimes%2010%5E%7B-6%7D%20C)
Kinetic energy of particle=![K_E=6.65\times 10^{-10} J](https://tex.z-dn.net/?f=K_E%3D6.65%5Ctimes%2010%5E%7B-10%7D%20J)
Initial time=![t_1=6.36 s](https://tex.z-dn.net/?f=t_1%3D6.36%20s)
Final potential difference=![V_2=0.351 V](https://tex.z-dn.net/?f=V_2%3D0.351%20V)
We have to find the time t after that the particle is released and traveled through a potential difference 0.351 V.
We know that
![qV=K.E](https://tex.z-dn.net/?f=qV%3DK.E)
Using the formula
![2.74\times 10^{-6}V_1=6.65\times 10^{-10} J](https://tex.z-dn.net/?f=2.74%5Ctimes%2010%5E%7B-6%7DV_1%3D6.65%5Ctimes%2010%5E%7B-10%7D%20J)
![V_1=\frac{6.65\times 10^{-10}}{2.74\times 10^{-6}}=2.43\times 10^{-4} V](https://tex.z-dn.net/?f=V_1%3D%5Cfrac%7B6.65%5Ctimes%2010%5E%7B-10%7D%7D%7B2.74%5Ctimes%2010%5E%7B-6%7D%7D%3D2.43%5Ctimes%2010%5E%7B-4%7D%20V)
Initial voltage=![V_1=2.43\times 10^{-4} V](https://tex.z-dn.net/?f=V_1%3D2.43%5Ctimes%2010%5E%7B-4%7D%20V)
![\frac{\initial\;voltage}{final\;voltage}=(\frac{initial\;time}{final\;time})^2](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cinitial%5C%3Bvoltage%7D%7Bfinal%5C%3Bvoltage%7D%3D%28%5Cfrac%7Binitial%5C%3Btime%7D%7Bfinal%5C%3Btime%7D%29%5E2)
Using the formula
![\frac{V_1}{V_2}=(\frac{6.36}{t})^2](https://tex.z-dn.net/?f=%5Cfrac%7BV_1%7D%7BV_2%7D%3D%28%5Cfrac%7B6.36%7D%7Bt%7D%29%5E2)
![\frac{2.43\times 10^{-4}}{0.351}=\frac{(6.36)^2}{t^2}](https://tex.z-dn.net/?f=%5Cfrac%7B2.43%5Ctimes%2010%5E%7B-4%7D%7D%7B0.351%7D%3D%5Cfrac%7B%286.36%29%5E2%7D%7Bt%5E2%7D)
![t^2=\frac{(6.36)^2\times 0.351}{2.43\times 10^{-4}}](https://tex.z-dn.net/?f=t%5E2%3D%5Cfrac%7B%286.36%29%5E2%5Ctimes%200.351%7D%7B2.43%5Ctimes%2010%5E%7B-4%7D%7D)
![t=\sqrt{\frac{(6.36)^2\times 0.351}{2.43\times 10^{-4}}}](https://tex.z-dn.net/?f=t%3D%5Csqrt%7B%5Cfrac%7B%286.36%29%5E2%5Ctimes%200.351%7D%7B2.43%5Ctimes%2010%5E%7B-4%7D%7D%7D)
![t=241.7 s](https://tex.z-dn.net/?f=t%3D241.7%20s)
Hence, after 241.7 s the particle is released has it traveled through a potential difference of 0.351 V.
The movement of the tectonic plates is caused by convection currents in Earth´s mantle.
Answer: A) convection currents in Earth´s mantle.
I don’t think so because an ice cube melting needs heat and relies on temp while ooblecks transition from solid to quickly depends on force and speed