Question

1. the reactive power (in watts) of an ac circuit due to the inductance and/or capacitance is given by: p = visinθ where: θ is called the phase angle (measured in degrees) i is the current (measured in amps) v is the voltage (measured in volts) find θ given a voltage of 240v, a current of 1.70a and a power of 106w. 3 marks

Explanation:

Step1: Rearrange the power formula for sinθ

Given $P = VI\sin\theta$, we can solve for $\sin\theta$ as $\sin\theta=\frac{P}{VI}$.

Step2: Substitute the given values

Substitute $V = 240V$, $I = 1.70A$ and $P = 106W$ into the formula. So $\sin\theta=\frac{106}{240\times1.70}$.
First, calculate $240\times1.70 = 408$. Then $\sin\theta=\frac{106}{408}\approx0.2598$.

Step3: Find the value of θ

Since $\sin\theta\approx0.2598$, then $\theta=\sin^{- 1}(0.2598)$. Using a calculator, $\theta\approx15.6^{\circ}$.

Answer:

$\theta\approx15.6^{\circ}$