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a_sh-v [17]
3 years ago
9

A battery has a terminal voltage of 12.0 V when no current flows. Its internal resistance is 2.0 Ω. If a 7.2 Ω resistor is conne

cted across the battery terminals, what is the terminal voltage and what is the current through the 7.2 Ω resistor?
Physics
1 answer:
Simora [160]3 years ago
7 0

Answer:

Voltage= 9.4 V

Current= 1.3 A

Explanation:

Equivalent resistance will be the sum of two resistors hence

R_{equ}=2+7.2=9.2Ω

From Ohm's law, V=IR where I is current, R is equivalent resistance and V is voltage

Terminal voltage will be given by V=e-Ir where r is internal resistance, I is current and e is electromotive force.

From Ohm's law, current is given by dividing emf of the battery by the equivalent resistance hence

I=\frac {e}{R_{equ}}\\I=\frac {12}{9.2}=1.304347826A\approx 1.3A

This is the current through external resistor

Terminal voltage will be given by V=e-Ir hence V=12-(1.3*2)=9.4 V

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A practical rule is that a radioactive nuclide is essentially gone after 10 half-lives. What percentage of the original radioact
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Answer:

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The equation for radioactive decay its:

N ( t) \ = \ N_0 \ e^{ \ -  \frac{t}{\tau}},

where N(t) its quantity of material at time t, N_0 its the initial quantity of material and \tau its the mean lifetime of the radioactive element.

The half-life t_{\frac{1}{2}} its the time at which the quantity of material its the half of the initial value, so, we can find:

N (t_{\frac{1}{2} }) \ = \ N_0 \ e^{ \ -  \frac{t_{\frac{1}{2}}}{\tau}} \ = \frac{N_0}{2}

so:

\ N_0 \ e^{ \ -  \frac{t_{\frac{1}{2}}}{\tau}} \ = \frac{N_0}{2}

e^{ \ -  \frac{t_{\frac{1}{2}}}{\tau}} \ = \frac{1}{2}

-  \frac{t_{\frac{1}{2}}}{\tau}} \ = - \ ln( 2 )

t_{\frac{1}{2}}\ = \tau ln( 2 )

So, after 10 half-lives, we got:

N ( 10 \  t_{\frac{1}{2}}) \ = \ N_0 \ e^{ \ -  \frac{10 \  t_{\frac{1}{2}}}{\tau}}

N ( 10 \  t_{\frac{1}{2}}) \ = \ N_0 \ e^{ \ -  \frac{10 \  \tau \ ln( 2 ) }{\tau}}

N ( 10 \  t_{\frac{1}{2}}) \ = \ N_0 \ e^{ \ -  10 \  \ ln( 2 ) }

N ( 10 \  t_{\frac{1}{2}}) \ = \ N_0 \ * \ 9.76 * 10^{-4}

So, we got that a 0.09 % of the original radioactive nucllde its left.

Putonioum-239 has a half-life of 24,110 years. So, 10 half-life will take to pass

10 \ * \ 24,110 \ years \ = \ 241,100 \ years

It will take 241,100 years for 10 half-lives of plutonium-239 to pass.

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