Two wires of same material and having length in the ratio 2 is to 3 are connected in series the potential difference across the wires are 4.2 volt and 3.6 volt respectively compare the radius
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sumit8648
22.04.2019
Physics
Secondary School
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two wires of same material and having length in the ratio 2 : 3 are connected in series the potential difference across the wires are 4.2 volt 3.6 volt respectively the ratio of their radii
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abhi178
abhi178 Genius
Let I is the current through wires which are connected in series combination.
so, resistance on first wire, R_1 = \frac{V_1}{I}
= 4.2/I .....(1)
resistance on 2nd wire, R_2=\frac{V_2}{I}
= 3.6/I ..... (2)
using formula of resistance, R = pl/A
where , p is resistivity , l is length and A is cross sectional area.
as, both wires are made of same material so, resistivities of both are same.
cross section area of first wire, A_1=\pi r_1^2
cross sectional area of 2nd wire, A_2=\pi r_2^2
now, R_1=p\frac{2l}{\pi r_1^2}
and R_2=p\frac{3l}{\pi r_2^2}
from equations (1) and (2),
\frac{R_1}{R_2}=\frac{4.2}{3.6}=\frac{2\pi r_2^2}{3\pi r_1^2}
or, \frac{7}{6}=\frac{2r_2^2}{3r_2^2}
or, \frac{7}{4}=\frac{r_2^2}{r_1^2}
hence, \frac{r_1}{r_2}=\sqrt{\frac{4}{7}}
so, answer is 2 : √7
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yadavpriyank00
yadavpriyank00 Ambitious
Answer:
Explanation:
Let I is the current through wires which are connected in series combination.
so, resistance on first wire,
= 4.2/I .....(1)
resistance on 2nd wire,
= 3.6/I ..... (2)
using formula of resistance, R = pl/A
where , p is resistivity , l is length and A is cross sectional area.
as, both wires are made of same material so, resistivities of both are same.
cross section area of first wire,
cross sectional area of 2nd wire,
now,
and
from equations (1) and (2),
or,
hence,
so, answer is 2 : √
Explanation:
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