CAIE A-Level Physics A2 21.1.2 Equations of the Form X X0 Sin T Representing a Sinusoidally Alternating

[Maximum number: 6]

(a)

Two coils of insulated wire are wound on an iron bar, as shown in Fig. 8.1.

Fig. 8.1

There is a current $I_{1}$ in coil 1 that varies with time t as shown in Fig. 8.2.

Fig. 8.2

[ 6 ]

(i)

The variation with t of $I_{1}$ can be represented by the equation

I_{1}=X \sin Y t

where X and Y are constants.

Use Fig. 8.2 to determine the values of X and Y. Give units with your answers.

\begin{aligned} & X=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . . . . . . . . . . . . . . . . u n i t \\ & Y=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . . . . . . . . . . . . . . . u n i t \end{aligned}

[ 3 ]

$X=0.85 \mathrm{~A}$ $Y=2 \pi / 0.040$ $=160 \mathrm{rad} \mathrm{s}^{-1}$

(ii)

The current in coil 1 gives rise to a magnetic field in the iron bar.

Assume that the flux density of this magnetic field is proportional to $I_{1}$ .
An alternating electromotive force (e.m.f.) is induced across coil 2. The p.d. across coil 2 is measured using the voltmeter and has a root-mean-square (r.m.s.) value of 4.6 V .

On Fig. 8.3, sketch a line to show the variation with t of $V_{2}$ between t=0 and $t=0.08 \mathrm{~s}$ .

Fig. 8.3

[ 3 ]

two cycles of a sinusoidal curve with a period of 0.040 s
correct phase (i.e. $V_{2} \max / \min$ at t=0,0.02,0.04,0.06 and 0.08 s , and $V_{2}$ zero at $t=0.01,0.03,0.05,0.07 \mathrm{~s}$ )
maximum / minimum $V_{2}$ shown (consistently) at $\pm 6.5 \mathrm{~V}$

CAIE A-Level Physics A2 21.1.2 Equations of the Form X X0 Sin T Representing a Sinusoidally Alternating Topic Practice

Question 1

Question (a)

Question (i)

Question (ii)