Current Electricity Part 2

For case I,
The potential difference of the uniform wire, V =240 V
The resistance of the uniform wire, R1 = 36 Ω
The power dissipation in the first case,
P1=

V2

R1

=

(240)2

36

For case II,
The resistance of each half, R2=

R1

2

=

36

2

=18Ω
P2=

V2

R2

+

V2

R2

=

(240)2

18

+

(240)2

18

=

(240)2

9

Thus, the ratio of the total power dissipation in the first case to thesecond case

P1

P2

=

(240)2∕36

(240)2∕9

⇒

P1

P2

=

1

4

Comparing with,

P1

P2

=

1

x

The value of the x = 4.