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When a resistance R is connected in seri...

When a resistance R is connected in series with an element A, the electric current is found to be lagging behind the voltage by angle `theta_(1)`. When the same resistanceis connected in series with element B, current leads voltage by `theta_(2)`. When R, A, B are connected in series, the current now leads voltage by theta. Assume same AC source is used in all cases, then:

A

`theta=theta_(2)-theta_(1)`

B

`tan theta=tan theta_(2)-tantheta_(1)`

C

`theta=(theta_(1)+theta_(2))/2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`tan theta_(1)=X_(L)/R …(1)`
`tan theta_(2)=X_(C )/R …(2)`
`tantheta=(X_(C )-X_(L))/R`
`tantheta=X_(C )/R-X_(L)/R …(3)`
from `(1), (2)` and `(3) tantheta=tantheta_(2)-tantheta_(1)`
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