Practical circuits
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Define electromotive force (e.m.f.).
Electromotive force (e.m.f.) is the total energy transferred per unit charge in driving charge around a complete circuit. It is measured in volts (V) and represents the potential difference provided by a source.
Explain the difference between e.m.f. and potential difference (p.d.) in terms of energy considerations.
E.m.f. is the energy supplied *by* a source per unit charge, whereas potential difference is the energy dissipated *by* a component per unit charge. E.m.f. is a source of energy, while p.d. represents energy used.
What effect does the internal resistance of a source have on the terminal potential difference?
Internal resistance causes the terminal potential difference to be less than the e.m.f. When current flows, some potential is 'lost' across the internal resistance (V = Ir), reducing the voltage available to the external circuit.
State Kirchhoff’s first law and explain its significance.
Kirchhoff's first law (junction rule) states that the total current entering a junction equals the total current leaving the junction. This is a direct consequence of the conservation of charge.
State Kirchhoff’s second law and explain its significance.
Kirchhoff's second law (loop rule) states that the sum of the e.m.f.s in a closed loop is equal to the sum of the potential drops. This law is a direct consequence of the conservation of energy.
Derive the formula for the combined resistance of two resistors in series using Kirchhoff's laws.
In series, the current is the same through both resistors. Using Kirchhoff's second law: V = V₁ + V₂ = IR₁ + IR₂ = I(R₁ + R₂). Therefore, the equivalent resistance is R = R₁ + R₂.
Derive the formula for the combined resistance of two resistors in parallel using Kirchhoff's laws.
In parallel, the voltage is the same across both resistors. Using Kirchhoff's first law: I = I₁ + I₂ = V/R₁ + V/R₂ = V(1/R₁ + 1/R₂). Therefore, 1/R = 1/R₁ + 1/R₂.
A battery with an e.m.f. of 6.0 V and an internal resistance of 0.5 Ω is connected to a 2.5 Ω resistor. Calculate the terminal potential difference.
First, find the current: I = e.m.f. / (R + r) = 6.0 / (2.5 + 0.5) = 2.0 A. Then, calculate the terminal potential difference: V = IR = 2.0 * 2.5 = 5.0 V.
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