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Standard XII

Physics

Coupling

Two coils, 1 ...

Question

Two coils, 1 and 2 have a mutual inductance $M = 5 H$ and resistance $R = 10 Ω$ each. A current flows in coil 1, which varies with time as: $I_{1} = 2 t^{2}$ , where t is time. Find the total charge (in $C$ ) that has flown through coil 2 between $t = 0$ and $t = 2 s$ .

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Solution

The correct option is A $4$
emf in second coil, at time $t$ is $E = M \frac{d I_{1}}{d t} = 4 M t$
current at time t in second loop is $\frac{E}{R}$
total charge flown through second coil in $2$ seconds = $\int_{0}^{2} \frac{4 M t}{R} d t = 4 C$

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A coil of wire having finite inductance and resistance has a conducting ring placed coaxially within it. The coil is connected to a battery at time t = 0, so that a time-dependent current $I_{1} (t)$ starts flowing through the coil. If $I_{2} (t)$ is the current induced in the ring and B(t) is the magnetic field at the axis of the coil due to $I_{1} (t)$ , then the product of $I_{2} (t)$ and B(t)

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Two coils, 1 and 2 have a mutual inductance M=5H and resistance R=10Ω each. A current flows in coil 1, which varies with time as: I1=2t2, where t is time. Find the total charge (in C) that has flown through coil 2 between t=0 and t=2s.

The correct option is A 4emf in second coil, at time t is E=MdI1dt=4Mtcurrent at time t in second loop is ERtotal charge flown through second coil in 2 seconds = ∫204MtRdt=4C

Two coils, 1 and 2 have a mutual inductance $M = 5 H$ and resistance $R = 10 Ω$ each. A current flows in coil 1, which varies with time as: $I_{1} = 2 t^{2}$ , where t is time. Find the total charge (in $C$ ) that has flown through coil 2 between $t = 0$ and $t = 2 s$ .

The correct option is A $4$
emf in second coil, at time $t$ is $E = M \frac{d I_{1}}{d t} = 4 M t$
current at time t in second loop is $\frac{E}{R}$
total charge flown through second coil in $2$ seconds = $\int_{0}^{2} \frac{4 M t}{R} d t = 4 C$