Television choices: Do rock stars really persuade us to donate to good causes?

TV pick of the week

Why Poverty? Give Us the Money

Sunday 9pm BBC4

It's now nearly 30 years since Bono and Bob Geldof (both left) began their campaign to end poverty in Africa – their rock-star agit prop evolving into a $30m lobbying organisation that has the ears of Obama and Putin as well as the likes of Bill Gates – the Microsoft billionaire participating in Bosse Lindquist's Storyville documentary (which opens the BBC's "Why Poverty?" season) that asks the simple question: does celebrity- led activism actually make any difference? The answer is less straightforward, supporters pointing to such initiatives as debt cancellation, while critics accuse the pair of arrogance. "If their goal really is poverty reduction and economic growth," says one, "then they've failed miserably."

The Killing III

Saturday 9pm & 10pm BBC4

The actress Sofie Grabol has always actively resisted romantic storylines, and if her burgeoning relationship with colleague Matthias is anything to go by, she has been right to. That aside, the Danish drama continues to exert its grip as the killer reponds to his latest execution. "The next time you consider paying small change for the life of a little girl, remember this."

Dying for Clear Skin

Monday 9pm & 12.30am BBC3

The lively Radio 1 breakfast DJ (if that isn't tautological) Gemma Cairney (above) turns reporter for this look at a skin condition that most teenagers endure as an inconvenient, slightly embarrassing rite-of-passage. Severe acne – or rather its psychological effects – can be fatal, and Cairney is joined by the father of a teenage boy whose disfiguring spots had tragic consequences.

The Dark Ages: An Age of Light

Tuesday 9pm BBC4

Waldemar Januszczak, trying a bit too hard to make his subject accesible, argues that the Dark Ages were a time of great artistic achievement. Or, as he puts it, "those misunderstood creatives, the barbarians... what wondrous bling they brought into the world." First stop, Rome's catacombs, and the sometimes puzzling art of the early Christians.

Secret State

Wednesday 10pm Channel 4

"You get to the top and you realise it's only really the middle," PM Tom Dawkins (Gabriel Byrne) concludes – as does this poorly scheduled re-imagining of A Very British Coup. As doubts arise from Dawkins's army service in Bosnia, the pressure to attack Iran is intensifying. But why does everyone insist on sharing state secrets in broad daylight on the Thames Embankment?

Captive – The Sex Slave Girl: True Stories

Thursday 10pm Channel 4

A lurid title for the extraordinary tale of 14-year-old Tanya Kach (above), who was held captive for 10 years by the school security guard, Thomas Hose, near her home in Pennsylvania. Kach, confined to Hose's bedroom for four years, was eventually introduced to his parents as his girlfriend and allowed on trips out – Hose's first mistake...

The Beach Boys: Doin' it Again

Friday 9pm & 1.05am BBC4

A documentary about the Beach Boys' 2012 reunion, commemorating the band's 50th year – but the good vibrations recorded here proved illusory, as the singer Mike Love sacked the other members (including the founder members Brian Wilson and Al Jardine) soon after it was made. The film kick-starts an evening programme dedicated to the California surf-pop sorts.