Ch 2 · 21 Alternating Currents · A Level Physics 9702
Topic 2 of 2 in Magnetic Fields and Alternating Currents — A Level Physics 9702 — 47 lessons.
Introduction
The mains supply alternates, but your phone needs steady d.c. This topic describes alternating currents properly, explains what "230 V" on the mains really means, and shows how diodes and a capacitor turn a.c. into smooth d.c. (Syllabus topic 21: sections 21.1–21.2.)
Key ideas — 21.1 (a) Describing a.c.
A sinusoidal alternating current or voltage varies as
🧑🏫 Teacher's explanation
Imagine a pendulum swinging back and forth. At its furthest point, it has maximum displacement, but it doesn't stay there; it constantly changes direction. Alternating current (a.c.) behaves similarly. Instead of flowing in one direction like water in a pipe, the electrons 'slosh' back and forth. The voltage or current reaches a maximum positive value, drops to zero, reaches a maximum negative value, and returns to zero.
📖 Definitions
🔍 Worked example — Easy
A sinusoidal voltage is given by V = 325sin(100π t) V. Calculate the frequency and the peak voltage.
🔍 Worked example — Standard
An alternating current has a peak value of 10.0 A. Calculate the r.m.s. current I_r.m.s. and the mean power dissipated in a 5.00Omega resistor.
🔍 Worked example — Exam-style
A sinusoidal voltage V = V_0sinω t is applied to a resistor. If the peak voltage is 300 V and the frequency is 60 Hz, calculate the time taken for the voltage to reach its first peak.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Key ideas — 21.1 (b) Mean power and r.m.s. values
The power in a resistor is P = I^2R. As I varies, I^2 varies between 0 and I_0^2, averaging half its peak value. So for a sinusoidal a.c. in a resistive load:
🧑🏫 Teacher's explanation
Imagine you are pushing a child on a swing. If you push with a constant force, the child moves steadily. If you push in pulses (alternating), the child's motion is jerky. Even though the 'peak' force you apply might be very high, the 'average' effect on the child's motion depends on the overall energy transferred. In an alternating current, the current is constantly changing direction and magnitude, so using the 'peak' value to calculate power would be misleading because the current isn't always at that maximum.
📖 Definitions
🔍 Worked example — Easy
An alternating current has a peak value I_0 = 5.0 A. Calculate the r.m.s. current.
🔍 Worked example — Standard
A resistor of R = 100Omega is connected to an alternating voltage with a peak value V_0 = 300 V. Calculate the mean power dissipated in the resistor.
⚠️ Common errors
🧠 Quick check 1
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🎯 Exam question
Key ideas — 21.2 (a) Rectification
Rectification converts a.c. into d.c. (current in one direction only).
🧑🏫 Teacher's explanation
Imagine a swinging pendulum. Its motion goes back and forth (alternating). If you want to turn that into a motion that only goes forward, you need a mechanism that 'filters' the direction. In electricity, an alternating current (a.c.) constantly reverses direction. Rectification is the process of forcing this current to flow in only one direction, effectively turning a.c. into direct current (d.c.).
📖 Definitions
🔍 Worked example — Easy
A sinusoidal alternating voltage is given by V = 10 sin(100π t) V. Calculate the peak voltage V_0 and the r.m.s. voltage V_r.m.s..
🔍 Worked example — Standard
A half-wave rectifier uses a single diode. If the input a.c. has a frequency of 50 Hz, what is the frequency of the output rectified current?
🔍 Worked example — Exam-style
A full-wave bridge rectifier is used to convert a 12 V peak a.c. voltage into d.c. A capacitor is added to smooth the output. If the load resistance is R and the capacitance is C, which would result in a smoother (less fluctuating) output: increasing C or increasing R?
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — 21.2 (b) Smoothing
A capacitor connected in parallel with the load smooths the rectified output:
🧑🏫 Teacher's explanation
Imagine a water tank with a small tap at the bottom. If you pour water into the tank in rhythmic, sudden bursts (like the pulses of rectified current), the water level in the tank won't drop to zero immediately because the tank acts as a reservoir. The water level stays relatively steady, providing a constant flow to the tap despite the uneven input. In electronics, the capacitor is that reservoir.
📖 Definitions
🔍 Worked example — Easy
A half-wave rectifier uses a single diode. A capacitor is added in parallel with the load. If the load resistance is R and the capacitance is C, write the expression for the time constant tau and state how increasing C affects the ripple voltage.
🔍 Worked example — Exam-style
A smoothing capacitor is used in a full-wave rectifier. The load resistance is 1000 Omega and the capacitance is 2000 muF. Calculate the time constant tau and explain why the ripple is smaller in a full-wave rectifier compared to a half-wave rectifier with the same R and C.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Worked example
Example 1. A sinusoidal p.d. has a peak of 17 V. Find its r.m.s. value, and the mean power in a 10 Ω resistor. V_r.m.s. = 17/sqrt2 = 12 V; langle Prangle = 12^2/10 = 14.4 W (or tfrac12 × 17^2/10 = 14.4 W).
🔍 Worked example — Easy
A sinusoidal voltage has a peak value of V_0 = 311 V. Calculate the r.m.s. voltage and the mean power dissipated in a 50 Omega resistor.
🔍 Worked example — Standard
An alternating current is described by the equation I = 4.0sin(100π t) A. Determine the peak current I_0, the frequency f, and the r.m.s. current I_r.m.s..
🔍 Worked example — Exam-style
A sinusoidal voltage V = V_0sin(ω t) is applied across a resistor R. If the maximum power delivered to the resistor is 200 W, calculate the mean power delivered to the resistor.
⚠️ Common errors
Common mistakes
Practice
Answers: (1) The value of the steady direct current that would dissipate the same mean power in a resistor. (2) 325 V; 0.020 s. (3) Half-wave: positive half-cycles separated by gaps; full-wave: continuous positive humps. (4) Four diodes are arranged so that in each half-cycle a different pair conducts, sending the current through the load in the same direction both times. (5) Use a larger capacitance or a larger load resistance (larger RC), or full-wave instead of half-wave rectification.