Question

Magnetic flux passing through a coil of resistance $2\Omega$ is as shown in figure. Match the following two columns. In column II all physical quantities are in $SI$ units.


$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(a) Induced emf produced}& \text{(p) 4}\\ \text{(b) Induced current}& \text{(q) 1}\\ \text{(c) Charge flow in 2 s}& \text{(r) 8}\\ \text{(d) Heat generation in 2 s}& \text{(s) 2}\end{array}$

• A. $\text{a}\to \text{s};\text{b}\to \text{q};\text{c}\to \text{s};\text{d}\to \text{p}$
• B. $\text{a}\to \text{q};\text{b}\to \text{q};\text{c}\to \text{s};\text{d}\to \text{q}$
• C. $\text{a}\to \text{r};\text{b}\to \text{q};\text{c}\to \text{s};\text{d}\to \text{q}$
• D. $\text{a}\to \text{p};\text{b}\to \text{q};\text{c}\to \text{s};\text{d}\to \text{q}$

Answer 1

The correct option is A $\text{a}\to \text{s};\text{b}\to \text{q};\text{c}\to \text{s};\text{d}\to \text{p}$

From the figure we can say that, $\varphi =2t$

Case-1: $e=\frac{d\varphi }{dt}=2\text{V}$

Case-2: $i=\frac{e}{R}=1\text{A}$

Case-3: $\Delta q=i\Delta t=1\times 2=2\text{C}$

Case-4: $H=i^{2}R\Delta t=(1{)}^2\times (2)\times (2)=4\text{J}$