Manipal Entrance Test 2015 Physics Paper

The general equations of alternating voltage and current in an AC circuit are as follows
E=E0‌sin‌ω‌t ...(i)
I=I0‌sin‌ω‌t ...(ii)
Given that,
E=100‌sin‌100‌π‌t ...(iii)
I=5‌sin‌100‌π‌t ...(iv)
Comparing Eqs. (ii) and and (iv), we get,
Peak value of current, I0 = 5A
Comparing Eqs. (i) and (iii), we get
Peak value of voltage, E0 = 100 V
Now, r.m.s. value of voltage is given by
Erms=

E0

√2

=

100

√2

V
Similarly, r.m.s. value of current is given by
Irms=

I0

√2

=

5

√2

A
Hence, reactance of the circuit is given by
Z=

Erms

Irms

=

100∕√2

5∕√2

=20Ω