A wire of radius r and another wire of radius 2 r, both of same material and length are connected in series to each other. The combination is connected across a battery. The ratio of the heats produced in the two wires will be

Question

A wire of radius r and another wire of radius 2 r, both of same material and length are connected in series to each other. The combination is connected across a battery. The ratio of the heats produced in the two wires will be (A) 4.00 (B) 2.00 (C) 0.50 (D) 0.25

Tardigrade Admin · Accepted Answer

H = I 2 Rt. Here R 1=ρ ( l /π r 2) and R 2=ρ (1/π(2 r )2) That is, R 1=4 R 2. Hence, ( H 1/ H 2)=4

Q. A wire of radius $r$ and another wire of radius $2 r$ , both of same material and length are connected in series to each other. The combination is connected across a battery. The ratio of the heats produced in the two wires will be

$4.00$

$2.00$

$0.50$

$0.25$

$H = I^{2} Rt$ .
Here $R_{1} = ρ \frac{l}{π r ^{2}}$ and $R_{2} = ρ \frac{1}{π ( 2 r ) ^{2}}$
That is, $R_{1} = 4 R_{2}$ .
Hence, $\frac{H _{1}}{H _{2}} = 4$

Q. A wire of radius r and another wire of radius 2r, both of same material and length are connected in series to each other. The combination is connected across a battery. The ratio of the heats produced in the two wires will be

4.00

2.00

0.50

0.25