The solar panels on the roof of a house measure 4.0 m by 6.0 m. Assume they convert 12 % of the

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The solar panels on the roof of a house measure 4.0 m by 6.0...

The solar panels on the roof of a house measure $4.0 \mathrm{m}$ by $6.0 \mathrm{m}$. Assume they convert $12 \%$ of the incident EM wave's energy to electric energy. (a) What average power do the panels supply when the incident intensity is $1.0 \mathrm{kW} / \mathrm{m}^{2}$ and the panels are perpendicular to the incident light? (b) What average power do the panels supply when the incident intensity is $0.80 \mathrm{kW} / \mathrm{m}^{2}$ and the light is incident at an angle of $60.0^{\circ}$ from the normal? (c) Take the average daytime power requirement of a house to be about $2 \mathrm{kW}$. How do your answers to (a) and (b) compare? What are the implications for the use of solar panels?

The solar panels on the roof of a house measure $4.0 \mathrm{m}$ by $6.0 \mathrm{m}$. Assume they convert $12 \%$ of the incident EM wave's energy to electric energy.
(a) What average power do the panels supply when the incident intensity is $1.0 \mathrm{kW} / \mathrm{m}^{2}$ and the panels are perpendicular to the incident light? (b) What average power do the panels supply when the incident intensity is $0.80 \mathrm{kW} / \mathrm{m}^{2}$ and the light is incident at an angle of $60.0^{\circ}$ from the normal? (c) Take the average daytime power requirement of a house to be about $2 \mathrm{kW}$. How do your answers to
(a) and (b) compare? What are the implications for the use of solar panels?

Key Concepts

Power Output and Consumption Comparison

The power output from solar panels is determined by the product of the incident intensity, effective area, and conversion efficiency. Comparing this calculated output to typical power consumption, such as the average daytime power requirement of a house, helps assess the practicality and limitations of solar power installations. This comparison informs decisions about the number of panels needed and the feasibility of solar energy as a primary electricity source.

Incident Intensity

Incident intensity is the power per unit area delivered by an electromagnetic wave onto a surface. It defines how much energy from the source falls on a surface and is typically measured in units such as watts per square meter (W/m²). In the context of solar panels, the incident intensity dictates the potential energy available for conversion into electrical power.

Effective Area and Projected Area

The effective area, or projected area, is the component of the panel's surface area that is effectively exposed to the incoming radiation. When light strikes a surface at an angle, the effective area is reduced by the cosine of the angle between the incident light and the normal to the surface. This concept is essential to accurately determine the amount of energy captured when the surface is not perpendicular to the radiation.

Conversion Efficiency

Conversion efficiency refers to the fraction of incident electromagnetic energy that is successfully converted into usable electrical energy by the solar panels. It accounts for losses due to factors such as heat and reflection, and is typically expressed as a percentage. A higher efficiency means more of the sunlight is transformed into electricity, which is crucial for evaluating the performance of solar energy systems.

Cosine Law for Incidence Angle

The cosine law for the incidence angle describes how the energy captured by a surface decreases as the angle of incidence increases. Specifically, the effective energy received is proportional to the cosine of the angle between the incoming light and the normal to the surface. This mathematical relationship is important in solar energy calculations, as it directly affects the power output when panels are tilted or when the sun is not directly overhead.

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